Drawing Angles
Semester 4B · Chapter 15 · Lesson 3 · MATH-4B-C15-L03
Before you begin: prerequisite check
Recall: 15.02. Attempt these questions independently first.
Measure the smaller indicated angle between the two rays, in degrees.
Show answer and reasoning
Align the protractor at the vertex and read from the baseline: 140°.
Measure the smaller indicated angle between the two rays, in degrees.
Show answer and reasoning
Align the protractor at the vertex and read from the baseline: 165°.
Measure the smaller indicated angle between the two rays, in degrees.
Show answer and reasoning
Align the protractor at the vertex and read from the baseline: 155°.
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
Constructing an angle is different from reading one that is already drawn. First draw a straight baseline ray from a labeled vertex. Align a protractor's center and zero baseline, locate the desired degree mark using the correct scale, and place a small point at that mark. Draw a second ray through the point and label the resulting angle. A measurement is acceptable only when the indicated interior region matches the requested turn. Leave enough physical space on the page for a ruler and protractor.
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
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.
Check 1: try it yourself
Using a protractor, construct an angle measuring 160°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 160°, draw second ray, and label.
Worked example 2
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.
Check 2: try it yourself
Using a protractor, construct an angle measuring 90°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 90°, draw second ray, and label.
Worked example 3
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.
Check 3: try it yourself
Using a protractor, construct an angle measuring 70°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 70°, draw second ray, and label.
Guided practice
Using a protractor, construct an angle measuring 65°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 65°, draw second ray, and label.
Using a protractor, construct an angle measuring 95°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 95°, draw second ray, and label.
Using a protractor, construct an angle measuring 80°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 80°, draw second ray, and label.
Using a protractor, construct an angle measuring 170°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 170°, draw second ray, and label.
Using a protractor, construct an angle measuring 120°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 120°, draw second ray, and label.
Independent practice
Using a protractor, construct an angle measuring 135°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 135°, draw second ray, and label.
Using a protractor, construct an angle measuring 105°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 105°, draw second ray, and label.
Using a protractor, construct an angle measuring 60°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 60°, draw second ray, and label.
Using a protractor, construct an angle measuring 75°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 75°, draw second ray, and label.
Using a protractor, construct an angle measuring 110°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 110°, draw second ray, and label.
Using a protractor, construct an angle measuring 20°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 20°, 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.
Using a protractor, construct an angle measuring 100°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 100°, draw second ray, and label.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Using a protractor, construct an angle measuring 60°. Label its vertex and both rays. Explain which turn or benchmark you used.
Show answer and reasoning
Check placement of the center and zero baseline; mark 60°, draw second ray, and label. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
A learner claims: “To draw a 60° angle, I can place the protractor anywhere on the page and mark 60°.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: its center must sit on the vertex and the zero baseline must align with the first ray. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Using a protractor, construct an angle measuring 30°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 30°, draw second ray, and label.
Using a protractor, construct an angle measuring 165°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 165°, draw second ray, and label.
Using a protractor, construct an angle measuring 50°. Label its vertex and both rays.
Show answer and reasoning
Check placement of the center and zero baseline; mark 50°, draw second ray, and label.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.