In triangle XYZ, m∠Z = (2m − 12)° and the exterior angle to ∠Z measures (3m + 7)°. Determine the value of m.
a) m = 42
b) m = 37
c) m = 19
d) m = 2.6
The exterior angle to ∠Z is formed by the extension of one of the sides of triangle XYZ. The sum of the measures of an interior angle and its corresponding exterior angle is always 180 degrees. Therefore, we have:
(2m − 12)° + (3m + 7)° = 180°
5m - 5 = 180
5m = 185
m = 37
Therefore, the value of m is 37 degrees. The correct option is b) m = 37.