Reflex Angles
Semester 4B · Chapter 15 · Lesson 5 · MATH-4B-C15-L05
Before you begin: prerequisite check
Recall: 15.04. Attempt these questions independently first.
An angle of 84° 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 84 from 180.
An angle of 60° 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 60 from 180.
An angle of 50° 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 50 from 180.
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
A reflex angle measures more than 180° and less than 360°. Two rays form a smaller turn and a larger turn around the same vertex. If the smaller angle is 75°, the reflex angle is 360°−75°=285°. The word reflex refers to which turn is measured, not how long the rays are. Draw a curved arrow around the outside of the smaller region to mark the reflex angle. A 75° angle is acute; its 285° complement around a full turn is reflex.
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
The smaller angle between two rays is 94°. Find their reflex angle.
Reflex angle = 360°−94°=266°. Mark the outside turn.
Check 1: try it yourself
The smaller angle between two rays is 71°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−71°=289°. Mark the outside turn.
Worked example 2
The smaller angle between two rays is 136°. Find their reflex angle.
Reflex angle = 360°−136°=224°. Mark the outside turn.
Check 2: try it yourself
The smaller angle between two rays is 93°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−93°=267°. Mark the outside turn.
Worked example 3
The smaller angle between two rays is 46°. Find their reflex angle.
Reflex angle = 360°−46°=314°. Mark the outside turn.
Check 3: try it yourself
The smaller angle between two rays is 117°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−117°=243°. Mark the outside turn.
Guided practice
The smaller angle between two rays is 131°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−131°=229°. Mark the outside turn.
The smaller angle between two rays is 29°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−29°=331°. Mark the outside turn.
The smaller angle between two rays is 118°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−118°=242°. Mark the outside turn.
The smaller angle between two rays is 157°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−157°=203°. Mark the outside turn.
The smaller angle between two rays is 148°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−148°=212°. Mark the outside turn.
Independent practice
The smaller angle between two rays is 159°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−159°=201°. Mark the outside turn.
The smaller angle between two rays is 163°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−163°=197°. Mark the outside turn.
The smaller angle between two rays is 92°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−92°=268°. Mark the outside turn.
The smaller angle between two rays is 52°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−52°=308°. Mark the outside turn.
The smaller angle between two rays is 87°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−87°=273°. Mark the outside turn.
The smaller angle between two rays is 33°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−33°=327°. Mark the outside turn.
The smaller angle between two rays is 123°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−123°=237°. Mark the outside turn.
The smaller angle between two rays is 133°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−133°=227°. Mark the outside turn.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
The smaller angle between two rays is 118°. Find their reflex angle. Explain which turn or benchmark you used.
Show answer and reasoning
Reflex angle = 360°−118°=242°. Mark the outside turn. The explanation must identify the selected angle region and use 90°, 180°, or 360° as appropriate.
A learner claims: “An angle of 240° is obtuse.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: 240° is reflex because it is larger than 180° and smaller than 360°. Explain the relevant quantities or properties, not merely the final answer.
Exit check
The smaller angle between two rays is 109°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−109°=251°. Mark the outside turn.
The smaller angle between two rays is 132°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−132°=228°. Mark the outside turn.
The smaller angle between two rays is 154°. Find their reflex angle.
Show answer and reasoning
Reflex angle = 360°−154°=206°. Mark the outside turn.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.