In triangle DEF, m∠D = (4x + 15)°, m∠E = (5x + 32)°, and m∠F = 70°. Determine the degree measure of the exterior angle to ∠D.
a) 137°
b) 113°
c) 67°
d) 43°
The sum of the measures of the interior angles of a triangle is 180°.
Therefore, (4x + 15)° + (5x + 32)° + 70° = 180°.
Combining like terms, 9x + 117° = 180°.
Subtracting 117° from both sides, 9x = 63°.
Dividing both sides by 9, x = 7°.
To find the degree measure of the exterior angle to ∠D, we subtract ∠D from 180°.
The degree measure of the exterior angle to ∠D is (4x + 15)° = (4*7 + 15)° = 43°.
Therefore, the correct answer is d) 43°.