Chapter 15: worked solutions and marking guide
37 review answers and 37 exam answers
Chapter review solutions
Classify a 180° angle as acute, right, obtuse, or straight.
Compare 180° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 165°.
Using a protractor, construct an angle measuring 85°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 85°, draw second ray, and label.
An angle of 27° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 27 from 180.
The smaller angle between two rays is 72°. Find their reflex angle.
Reflex angle = 360°−72°=288°. Mark the outside turn.
Classify a 100° angle as acute, right, obtuse, or straight.
Compare 100° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 135°.
Using a protractor, construct an angle measuring 25°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 25°, draw second ray, and label.
An angle of 149° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 149 from 180.
The smaller angle between two rays is 82°. Find their reflex angle.
Reflex angle = 360°−82°=278°. Mark the outside turn.
Classify a 145° angle as acute, right, obtuse, or straight.
Compare 145° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 75°.
Using a protractor, construct an angle measuring 70°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 70°, draw second ray, and label.
An angle of 80° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 80 from 180.
The smaller angle between two rays is 83°. Find their reflex angle.
Reflex angle = 360°−83°=277°. Mark the outside turn.
Classify a 135° angle as acute, right, obtuse, or straight.
Compare 135° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 150°.
Using a protractor, construct an angle measuring 35°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 35°, draw second ray, and label.
An angle of 102° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 102 from 180.
The smaller angle between two rays is 164°. Find their reflex angle.
Reflex angle = 360°−164°=196°. Mark the outside turn.
Classify a 70° angle as acute, right, obtuse, or straight.
Compare 70° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 105°.
Using a protractor, construct an angle measuring 140°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 140°, draw second ray, and label.
An angle of 71° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 71 from 180.
The smaller angle between two rays is 57°. Find their reflex angle.
Reflex angle = 360°−57°=303°. Mark the outside turn.
Classify a 15° angle as acute, right, obtuse, or straight.
Compare 15° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 110°.
Using a protractor, construct an angle measuring 115°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 115°, draw second ray, and label.
An angle of 77° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 77 from 180.
The smaller angle between two rays is 31°. Find their reflex angle.
Reflex angle = 360°−31°=329°. Mark the outside turn.
Classify a 155° angle as acute, right, obtuse, or straight.
Compare 155° to 90° and 180°. A ray length does not affect the turn.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 160°.
Classify a 95° angle as acute, right, obtuse, or straight. Explain which turn or benchmark you used.
Compare 95° to 90° and 180°. A ray length does not affect the turn. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Measure the smaller indicated angle between the two rays, in degrees. Explain which turn or benchmark you used.
Align the protractor at the vertex and read from the baseline: 70°. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Using a protractor, construct an angle measuring 75°. Label its vertex and both rays. Explain which turn or benchmark you used.
Check placement of the center and zero baseline; mark 75°, draw second ray, and label. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
An angle of 114° lies next to another angle on a straight line. Find the missing angle. Explain which turn or benchmark you used.
Adjacent angles along a straight line add to 180°. Subtract 114 from 180. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
The smaller angle between two rays is 31°. Find their reflex angle. Explain which turn or benchmark you used.
Reflex angle = 360°−31°=329°. Mark the outside turn. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Practice examination solutions
Using a protractor, construct an angle measuring 105°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 105°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
An angle of 116° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 116 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 95°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 40°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Classify a 60° angle as acute, right, obtuse, or straight.
Compare 60° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An angle of 26° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 26 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 163°. Find their reflex angle. Explain which turn or benchmark you used.
Reflex angle = 360°−163°=197°. Mark the outside turn. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Classify a 170° angle as acute, right, obtuse, or straight. Explain which turn or benchmark you used.
Compare 170° to 90° and 180°. A ray length does not affect the turn. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 30°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Using a protractor, construct an angle measuring 55°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 55°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
An angle of 105° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 105 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 133°. Find their reflex angle.
Reflex angle = 360°−133°=227°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 71°. Find their reflex angle.
Reflex angle = 360°−71°=289°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 147°. Find their reflex angle.
Reflex angle = 360°−147°=213°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees. Explain which turn or benchmark you used.
Align the protractor at the vertex and read from the baseline: 90°. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 45°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Classify a 105° angle as acute, right, obtuse, or straight.
Compare 105° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 125°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Classify a 160° angle as acute, right, obtuse, or straight.
Compare 160° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Using a protractor, construct an angle measuring 150°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 150°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
An angle of 42° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 42 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Using a protractor, construct an angle measuring 40°. Label its vertex and both rays. Explain which turn or benchmark you used.
Check placement of the center and zero baseline; mark 40°, draw second ray, and label. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
An angle of 112° lies next to another angle on a straight line. Find the missing angle. Explain which turn or benchmark you used.
Adjacent angles along a straight line add to 180°. Subtract 112 from 180. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
Scoring (3 points): 1 point for identifying the relevant property; 1 for a correct solution; 1 for reasoning.
Using a protractor, construct an angle measuring 145°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 145°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
Classify a 30° angle as acute, right, obtuse, or straight.
Compare 30° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Classify a 65° angle as acute, right, obtuse, or straight.
Compare 65° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 149°. Find their reflex angle.
Reflex angle = 360°−149°=211°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 84°. Find their reflex angle.
Reflex angle = 360°−84°=276°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Classify a 50° angle as acute, right, obtuse, or straight.
Compare 50° to 90° and 180°. A ray length does not affect the turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 100°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
The smaller angle between two rays is 119°. Find their reflex angle.
Reflex angle = 360°−119°=241°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Using a protractor, construct an angle measuring 135°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 135°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
An angle of 133° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 133 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Using a protractor, construct an angle measuring 40°. Label its vertex and both rays.
Check placement of the center and zero baseline; mark 40°, draw second ray, and label.
Scoring (4 points): 1 point for a correctly interpreted diagram or setup; 1 for a valid method; 1 for the result; 1 for clearly labeled construction/dimensions.
The smaller angle between two rays is 70°. Find their reflex angle.
Reflex angle = 360°−70°=290°. Mark the outside turn.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 140°.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.
An angle of 85° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 85 from 180.
Scoring (2 points): 1 point for a sound method and 1 point for a correct, labeled answer.