Angle Calculation Questions
Angle calculation questions ask you to use known angle facts to find a missing angle. The key is to recognise which total applies: 90°, 180°, or 360°.
The Rules Every Angle Question Uses
Most missing-angle questions are solved by matching the diagram to one of a few standard angle totals.
📐 Rule 1: Right angles total 90°
If a right angle is split into two parts, the two parts add to 90°.
Example: 61° and y make 90°, so y = 29°.
📏 Rule 2: Straight lines total 180°
Angles sitting on one straight line add to 180°.
Example: 31°, 50°, and z on a line give z = 99°.
🔺 Rule 3: Triangles total 180°
The three inside angles in a triangle always add to 180°.
Example: 35°, 35°, and x give x = 110°.
🔄 Rule 4: Around a point totals 360°
If angles meet all the way around a point, they add to a full turn.
Example: Subtract known angles from 360° to find the missing one.
How to Solve Angle Calculation Questions
Three useful moves: identify the angle fact, add the known angles, then subtract from the correct total.
1. Use a Right Angle
Question: What is the size of angle y?
Worked Method
Step 1: The two angles make a right angle, so they total 90°.
Step 2: Subtract the known angle: 90° - 61° = 29°.
Answer: y = 29°
2. Use Angles in a Triangle
Question: What is the size of angle x?
Worked Method
Step 1: The angles in a triangle total 180°.
Step 2: Add the known angles: 35° + 35° = 70°.
Step 3: Subtract from 180°: 180° - 70° = 110°.
Answer: x = 110°
3. Use the Whole Straight Line
Question: What is the size of angle z?
Worked Method
Step 1: The three angles sit on a straight line, so they total 180°.
Step 2: Add the two known angles: 31° + 50° = 81°.
Step 3: Subtract from 180°: 180° - 81° = 99°.
Answer: z = 99°. The trap: Do not subtract from 360° when the angles only sit on one straight line.
Before You Buy
Want to check the level and layout first? Download the free 3-question sample. It uses the same question style, printable format, and answer-key approach as the full pack.
Download Free Sample PDFGet the Full Practice Pack
The full Angles pack contains 75 angle calculation questions across 3 printable test sets, with answer sheets included for quick checking.
Checkout and downloads are securely handled on Etsy.com