Final answer:
Using the exterior angle theorem and the sum of angles in a triangle, we can set up an equation, solve it, and find that the value of m is 12 in triangle XYZ.
Step-by-step explanation:
In triangle XYZ, the measure of angle Z is given by m∠Z = (5m - 15)° and the measure of the exterior angle to ∠Z is given by (7m + 3)°. Since the exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles, we can set up an equation to determine the value of m.
We know that:
- m∠Z + the measure of the interior angle opposite to ∠Z = the exterior angle to ∠Z
Therefore:
(5m - 15)° + the measure of the interior angle opposite to ∠Z = (7m + 3)°
Since the sum of the angles in a triangle is 180°, the measure of the interior angle opposite to ∠Z can be represented by 180° - (5m - 15)°. Substituting this into our equation gives us:
(5m - 15)° + (180° - (5m - 15)°) = (7m + 3)°
Solving this for m yields:
m = 12