Geometry

Angles

Angle tasks look simple but often hide a small equation. Know the angle sums and the rules for parallel lines.

The rules

• Triangle: α + β + γ = 180°; quadrilateral: 360°; n-gon: (n − 2) · 180°.
• Vertical angles are equal; angles on a straight line add up to 180°.
• At parallel lines: corresponding and alternate angles are equal.
• Isosceles triangle: the base angles are equal.

Practice questions with solutions

Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.

1. 1. A triangle has two angles of 52° and 22°. What is the measure of the third angle?

   • a74
   • b106
   • c128
   • d116
   Show solution

   Answer: 106

   The interior angles of a triangle sum to 180°.

   180 − 52 − 22 = 106.

2. 2. What is the sum of the interior angles of a convex polygon with 7 sides?

   • a900
   • b1260
   • c1080
   • d450
   Show solution

   Answer: 900

   Sum of interior angles of an n-gon = (n − 2) × 180°.

   (7 − 2) × 180 = 900.

3. 3. What is the sum of the interior angles of a convex polygon with 10 sides?

   • a1800
   • b1620
   • c720
   • d1440
   Show solution

   Answer: 1440

   Sum of interior angles of an n-gon = (n − 2) × 180°.

   (10 − 2) × 180 = 1440.

4. 4. What is the sum of the interior angles of a convex polygon with 9 sides?

   • a1620
   • b1440
   • c630
   • d1260
   Show solution

   Answer: 1260

   Sum of interior angles of an n-gon = (n − 2) × 180°.

   (9 − 2) × 180 = 1260.

5. 5. A triangle has two angles of 63° and 24°. What is the measure of the third angle?

   • a117
   • b103
   • c87
   • d93
   Show solution

   Answer: 93

   The interior angles of a triangle sum to 180°.

   180 − 63 − 24 = 93.

6. 6. A triangle has two angles of 34° and 39°. What is the measure of the third angle?

   • a73
   • b107
   • c146
   • d117
   Show solution

   Answer: 107

   The interior angles of a triangle sum to 180°.

   180 − 34 − 39 = 107.

Common mistakes

• Using 360° for a triangle.
• Setting up the equation with the wrong relation, such as 'twice as large' the wrong way round.
• Assuming a triangle is isosceles when the task does not say so.

Related topics

All maths topics · T-Kurs · M-Kurs · W-Kurs