Measuring Angles
Semester 4B · Chapter 15 · Lesson 2 · MATH-4B-C15-L02
Before you begin: prerequisite check
Recall: 15.01. Attempt these questions independently first.
Classify a 115° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 115° to 90° and 180°. A ray length does not affect the turn.
Classify a 25° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 25° to 90° and 180°. A ray length does not affect the turn.
Classify a 175° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 175° to 90° and 180°. A ray length does not affect the turn.
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
To measure an angle, place the protractor's center exactly over the vertex and align its zero baseline with one ray. Follow the correct numbered scale from that ray's zero mark to the second ray. A ray at 40° on one scale might align with 140° on the other; choose based on the starting ray, not whichever number you see first. Check visually whether the measured angle is acute, right, or obtuse. This classification catches many scale-reading mistakes.
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
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 100°.
Check 1: try it yourself
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: 65°.
Worked example 2
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 145°.
Check 2: try it yourself
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: 115°.
Worked example 3
Measure the smaller indicated angle between the two rays, in degrees.
Align the protractor at the vertex and read from the baseline: 165°.
Check 3: try it yourself
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: 80°.
Guided practice
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: 20°.
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: 130°.
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: 40°.
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: 95°.
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: 70°.
Independent practice
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: 35°.
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: 75°.
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: 110°.
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: 25°.
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: 50°.
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: 45°.
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: 125°.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Measure the smaller indicated angle between the two rays, in degrees. Explain which turn or benchmark you used.
Show answer and reasoning
Align the protractor at the vertex and read from the baseline: 45°. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
A learner claims: “If the protractor shows 40 and 140 at a ray, it does not matter which scale is used.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: read the scale beginning at zero on the starting ray; angle size may be 40° or 140° depending on the baseline. Explain the relevant quantities or properties, not merely the final answer.
Exit check
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: 120°.
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: 55°.
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: 90°.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.