Question

in triangle xyz, m∠y = 38.25° and m∠z = 74.3°. determine the measure of the exterior angle to ∠x. 152.05° 112.55° 98.60° 62.05°

Explanation:

Step1: Find the measure of $\angle X$

The sum of angles in a triangle is $180^{\circ}$. So, $m\angle X=180^{\circ}-m\angle Y - m\angle Z$.
Substitute $m\angle Y = 38.25^{\circ}$ and $m\angle Z=74.3^{\circ}$:
$m\angle X=180^{\circ}-38.25^{\circ}-74.3^{\circ}=67.45^{\circ}$

Step2: Find the exterior angle to $\angle X$

The exterior angle of an angle is supplementary to it (sum to $180^{\circ}$).
Let the exterior angle be $E$. Then $E = 180^{\circ}-m\angle X$.
Substitute $m\angle X = 67.45^{\circ}$:
$E=180^{\circ}-67.45^{\circ}=112.55^{\circ}$

Answer:

$112.55^{\circ}$