Question

In triangle def, m∠d = (3x 27)°, m∠e = (4x 22)°, and m∠f = 68°. determine the degree measure of the exterior angle to ∠d. 54° 58° 122° 126°

Answer 1

It is known that the sum of all three angles inside a triangle will be 180°.

So, m∠D + m∠E + m∠F = 180°

(3x + 27) + (4x + 22) + 68 = 180

7x + 49 + 68 = 180

7x = 63

x = 9

So, m∠D = (3(9) + 27)° = 54°.

The exterior angle of D = 180- 54 = 126°.

Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".