Maths Library

Finding Angle Measures: Grade 10 math

This topic covers finding missing angles using fundamental geometric angle facts. The worksheet practises calculating unknown angles on a straight line, around a point, in triangles, and vertically opposite angles.

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What this covers

Finding Angle Measures is taught in Grade 10 (age 15 to 16) as a main teaching focus. It sits in the Geometry strand.

Worked example

Two angles lie on a straight line. One angle is 68 degrees. Find the missing angle x.

  1. Recall that angles on a straight line sum to 180 degrees
  2. Set up the equation: x + 68 = 180
  3. Subtract 68 from 180: x = 112

Answer: 112

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Complementary angles adding to 90 degrees and supplementary to 180 with two angles
  2. Angles on a straight line or at a point with three angles
  3. Missing angles inside scalene and isosceles triangles
  4. Vertically opposite angles combined with straight line rules
  5. Multi-step problems involving parallel line angle rules (alternate, corresponding)

Common mistakes

  • Assuming angles are equal simply because they look similar rather than applying rules
  • Using 360 degrees instead of 180 degrees for angles on a straight line

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • Prove and apply geometric theorems about lines and angles, including vertical angles and parallel lines cut by a transversal.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Finding Angle Measures

Grade 10 math

Qs
6
Marks
24
NameDateScore / 24
1.
Angles on a straight line add up to 180°. One angle is 71°. Find the other.
[4]
2.
Three angles around a point are 79°, 69° and 148°. Find the fourth angle.
[4]
3.
Find the sum of the interior angles of a polygon with 6 sides.
[4]
4.
Three angles around a point are 75°, 49° and 124°. Find the fourth angle.
[4]
5.
Three angles around a point are 46°, 44° and 90°. Find the fourth angle.
[4]
6.
Find the sum of the interior angles of a polygon with 5 sides.
[4]

Answer key

  1. 109°180 − 71 = 109
  2. 64°Angles around a point add up to 360°; 360 − 79 − 69 − 148
  3. 720°Sum = (n − 2) × 180; (6 − 2) × 180 = 720
  4. 112°Angles around a point add up to 360°; 360 − 75 − 49 − 124
  5. 180°Angles around a point add up to 360°; 360 − 46 − 44 − 90
  6. 540°Sum = (n − 2) × 180; (5 − 2) × 180 = 540