Practice Exterior Angle Theorem in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.

Imagine standing at one corner of a triangular park and looking along one side. The exterior angle is how far you'd turn to look back along the other side. That turn combines the 'bends' at the other two corners—it equals their angles added together.

Showing a random 20 of 50 problems.

Example 1

medium
In triangle ABC, side BC is extended to D. If ∠A=55°\angle A = 55° and ∠B=65°\angle B = 65°, find ∠ACD\angle ACD.

Example 2

easy
The exterior angle of a triangle is 130°. One remote interior angle is 70°. Find the other remote interior angle.

Example 3

easy
The exterior angle of a triangle equals the sum of which angles?

Example 4

medium
The exterior angle at a vertex is 140°, and the two remote interior angles are equal. Find each remote interior angle.

Example 5

medium
The 'turtle turning' interpretation: walking around a triangle, the total turning at the three corners is?

Example 6

easy
A triangle has interior angles 50° and 60° at two vertices. Find the exterior angle at the third vertex.

Example 7

easy
Two remote interior angles of a triangle measure 52°52° and 68°68°. Find the exterior angle at the third vertex.

Example 8

easy
How is the exterior angle theorem derived from the angle sum?

Example 9

challenge
In triangle ABC, an exterior angle at A equals 110°. The bisector of this exterior angle is drawn. What angle does the bisector make with side AB's extension, and what are the remote interiors' sum?

Example 10

medium
In △ABC\triangle ABC, ∠A=38°\angle A = 38° and ∠B=62°\angle B = 62°. Find the exterior angle at CC and the exterior angle at AA.

Example 11

hard
Prove using the angle-sum theorem that every exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

Example 12

easy
An exterior angle of a triangle is 80°80°. Can it be the exterior angle of a triangle whose remote interior angles are 40°40° and 50°50°?

Example 13

medium
In triangle ABC, the exterior angle at C is 3 times ∠A\angle A, and ∠B=40°\angle B = 40°. Find ∠A\angle A.

Example 14

medium
An isosceles triangle has a base angle of 50°. Find the exterior angle at the apex.

Example 15

medium
A triangle's exterior angles are extended at all three vertices. Use the exterior angle theorem to show their measures, if interiors are 50°, 60°, 70°.

Example 16

medium
In △ABC\triangle ABC, the exterior angle at CC measures 4x+10°4x + 10°. The remote interior angles measure 2x+5°2x + 5° and x+25°x + 25°. Find xx.

Example 17

easy
Two remote interior angles of a triangle are 25°25° and 90°90°. What is the exterior angle at the third vertex?

Example 18

medium
Two exterior angles of a triangle are 110°110° and 130°130°. Find the third exterior angle and all three interior angles.

Example 19

easy
Two remote interior angles of a triangle are 40° and 65°. What is the exterior angle at the third vertex?

Example 20

easy
One remote interior angle equals the exterior angle minus 40°40°, and the other remote interior angle is 40°40°. Find the exterior angle.
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