Find x Using the Triangle Exterior Angle Theorem

Published on October 4, 2026

Geometry

A triangle has a 35° vertex angle and a 65° angle vertical to its left interior angle. Use the exterior angle theorem to set 5x + 30 equal to 65 + 35, then solve to find x = 14.

Question

Answer

The triangle’s left interior angle is

because it is vertical to the marked angle. By the exterior angle theorem, the marked angle on the right is

Thus,

Theorems

• Vertical Angles Theorem

When two lines intersect, opposite (vertical) angles are equal: if

and

are vertical angles, then

• Exterior Angle Theorem

An exterior angle of a triangle equals the sum of its two opposite interior angles:

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