Triangle geometry

Question

Triangle ABC has an exterior angle adjacent to Angle A that measures (4x) degrees. Angle B measures 25 degrees and angle C measures (3x) degrees. What is the value of x? What is the measure of each of the three interior angles as well as the exterior angles?

Answer 1

The exterior angle (4x) is equal to the sum of the two non-adjacent interior angles (25 + 3x)

4x = 25 + 3x

x = 25

so the exterior angle is equal to 4(25) = 100

Angle C is equal to 3(25) = 75 degrees

Since the sum of the angles of a triangle is 180, m<A = 180 - 25 - 75 = 80