Adding and Subtracting Angles
Semester 4B · Chapter 15 · Lesson 4 · MATH-4B-C15-L04
Before you begin: prerequisite check
Recall: 15.01–15.03. Attempt these questions independently first.
Using a protractor, construct an angle measuring 125°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 125°, draw second ray, and label.
Using a protractor, construct an angle measuring 40°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 40°, draw second ray, and label.
Using a protractor, construct an angle measuring 115°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 115°, draw second ray, and label.
Key vocabulary
- vertex
- common endpoint of two rays
- degree
- unit for angular turn
- protractor
- tool measuring angles
- reflex angle
- turn greater than 180° but less than 360°
Understand the concept
Adjacent angles can combine to make a larger turn. If one angle is 35° and an adjacent one is 50°, the combined angle is 85°. Conversely, if adjacent angles make a straight line, their sum must be 180°; an unknown neighboring angle is 180° minus the known one. Angles around one point add to 360°. Use a diagram to decide whether you are adding pieces or subtracting from a whole turn. Label degree symbols on all answers.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
An angle of 53° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 53 from 180.
Check 1: try it yourself
An angle of 77° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 77 from 180.
Worked example 2
An angle of 145° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 145 from 180.
Check 2: try it yourself
An angle of 52° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 52 from 180.
Worked example 3
An angle of 95° lies next to another angle on a straight line. Find the missing angle.
Adjacent angles along a straight line add to 180°. Subtract 95 from 180.
Check 3: try it yourself
An angle of 91° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 91 from 180.
Guided practice
An angle of 121° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 121 from 180.
An angle of 103° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 103 from 180.
An angle of 131° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 131 from 180.
An angle of 39° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 39 from 180.
An angle of 144° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 144 from 180.
Independent practice
An angle of 33° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 33 from 180.
An angle of 62° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 62 from 180.
An angle of 64° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 64 from 180.
An angle of 75° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 75 from 180.
An angle of 137° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 137 from 180.
An angle of 56° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 56 from 180.
An angle of 88° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 88 from 180.
An angle of 148° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 148 from 180.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
An angle of 49° lies next to another angle on a straight line. Find the missing angle. Explain which turn or benchmark you used.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 49 from 180. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
A learner claims: “Two neighboring angles on a straight line are always equal.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: they sum to 180° but may differ. If one is 50°, the other is 130°. Explain the relevant quantities or properties, not merely the final answer.
Exit check
An angle of 38° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 38 from 180.
An angle of 97° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 97 from 180.
An angle of 153° lies next to another angle on a straight line. Find the missing angle.
Show answer and reasoning
Adjacent angles along a straight line add to 180°. Subtract 153 from 180.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.