Question

Triangle A B C. Point D extends from side A B. Angle A is 35 degrees, angle B is 90 degrees, and angle C is x degrees. Exterior angle D A C is y degrees. Consider triangle ABC with exterior angle ∠DAC. Find the missing angle measures

Answer 1

x = 55°

y = 145°

Explanation:

bc

Answer 2

x = 55°

y = 145°

Explanation:

The relations involved here are ...

• the sum of angles in a triangle is 180°
• the sum of angles in a linear pair is 180°

a)

Internal angles A, B, and C total 180°. That means ...

35° +90° +x = 180°

x = 55° . . . . . . . . . . . subtract 125°

__

b)

The linear pair of angles at A totals 180° That means ...

35° +y = 180°

y = 145° . . . . . . . subtract 35°