What can you call a triangle ABC if its outer angles are 117 and 126 degrees?

triangle ABC,

angle EAB – outer angle of triangle ABC,

angle ВСК – outer angle of triangle ABC,

angle EAB = 117 degrees,

ВСK angle = 126 degrees.

Find out what the ABC triangle can be called.

Decision:

Angle EAB and angle BAC are adjacent. Therefore, the sum of their degree measures is 180 degrees, that is, the angle EAB + angle BAC = 180, then the angle BAC = 180 – the angle EAB = 180 – 117 = 63 degrees.

The BCA angle and the BCA angle are adjacent. Therefore, the sum of their degree measures is equal to 180 degrees, that is, the BCA angle + BCA angle = 180, then BCA angle = 180 – BCA angle = 180 – 126 = 54 degrees.

Angle A + angle B + angle C = 180;

63 + angle B + 54 = 180;

angle B = 180 – 63 – 54;

angle B = 63 degrees.

Then triangle ABC is isosceles.

Answer: isosceles.