Question

In triangle xyz, m∠z = (5m - 16)° and the exterior angle to ∠z measures (3m 12)°. Determine the value of m.

1) 3
2) 10.8
3) 18
4) 23

Answer 1

After setting up and solving the equation based on the relationship between an interior angle and its corresponding exterior angle in a triangle, we find that the value of m is 23.

Step-by-step explanation:

To determine the value of m in the given triangle problem, we use the fact that the sum of the interior angle and its corresponding external angle of a triangle is equal to 180°. Given that m∠z = (5m - 16)° and the exterior angle to ∠z measures (3m + 12)°, we can set up an equation:

(5m - 16)° + (3m + 12)° = 180°.

Combining like terms, we get 8m - 4 = 180. Adding 4 to both sides gives us 8m = 184. Dividing both sides by 8 yields m = 23.

Thus, the value of m that satisfies the given conditions is 23.