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 always 180°.
Therefore, we can set up the equation:
(4x + 15)° + (5x + 32)° + 70° = 180°
Combining like terms, we get:
9x + 117 + 70 = 180
9x + 187 = 180
9x = -7
x = -7/9
Since x is negative, we can conclude that the degree measure of the exterior angle to ∠D is equal to:
(4x + 15)° = (4 * (-7/9) + 15)° = 81/9 - 28/9 = 53/9
Therefore, the degree measure of the exterior angle to ∠D is approximately 5.89°.
However, none of the options provided matches this value. Please double-check the given answer options.