The Size of Angles
Semester 4B · Chapter 15 · Lesson 1 · MATH-4B-C15-L01
Before you begin: prerequisite check
Recall: 3B basic angle classification. Attempt these questions independently first.
How many degrees are in a right angle?
Show answer and reasoning
A right angle is a quarter turn.
How many degrees are in a straight angle?
Show answer and reasoning
A straight angle is a half turn.
How many degrees are in one full turn?
Show answer and reasoning
A full turn is 360°.
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
An angle describes the amount of turn between two rays sharing a vertex, not the length of those rays. Changing how far you draw a ray does not change the angle. A full turn is 360°, a half-turn is 180°, and a quarter-turn is 90°. Acute angles are between 0° and 90°, right angles are 90°, obtuse angles are between 90° and 180°, and straight angles are 180°. Identify the intended interior angle before measuring it.
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
Classify a 20° angle as acute, right, obtuse, or straight.
Compare 20° to 90° and 180°. A ray length does not affect the turn.
Check 1: try it yourself
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.
Worked example 2
Classify a 50° angle as acute, right, obtuse, or straight.
Compare 50° to 90° and 180°. A ray length does not affect the turn.
Check 2: try it yourself
Classify a 15° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 15° to 90° and 180°. A ray length does not affect the turn.
Worked example 3
Classify a 170° angle as acute, right, obtuse, or straight.
Compare 170° to 90° and 180°. A ray length does not affect the turn.
Check 3: try it yourself
Classify a 100° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 100° to 90° and 180°. A ray length does not affect the turn.
Guided practice
Classify a 70° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 70° to 90° and 180°. A ray length does not affect the turn.
Classify a 180° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 180° to 90° and 180°. A ray length does not affect the turn.
Classify a 55° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 55° to 90° and 180°. A ray length does not affect the turn.
Classify a 60° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 60° 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.
Independent practice
Classify a 95° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 95° to 90° and 180°. A ray length does not affect the turn.
Classify a 145° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 145° to 90° and 180°. A ray length does not affect the turn.
Classify a 125° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 125° to 90° and 180°. A ray length does not affect the turn.
Classify a 75° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 75° to 90° and 180°. A ray length does not affect the turn.
Classify a 110° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 110° to 90° and 180°. A ray length does not affect the turn.
Classify a 130° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 130° to 90° and 180°. A ray length does not affect the turn.
Classify a 65° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 65° to 90° and 180°. A ray length does not affect the turn.
Classify a 165° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 165° to 90° and 180°. A ray length does not affect the turn.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Classify a 120° angle as acute, right, obtuse, or straight. Explain which turn or benchmark you used.
Show answer and reasoning
Compare 120° 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.
A learner claims: “A long ray always makes a bigger angle than a short ray.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: angle size measures turn between directions; ray length does not affect degree measure. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Classify a 40° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 40° to 90° and 180°. A ray length does not affect the turn.
Classify a 80° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 80° to 90° and 180°. A ray length does not affect the turn.
Classify a 150° angle as acute, right, obtuse, or straight.
Show answer and reasoning
Compare 150° to 90° and 180°. A ray length does not affect the turn.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.