Question

question 41 of 45
in the figure below, what is the value of x?
38°
x°
100°
a. 62°
b. 38°
c. 180°
d. 80°

Explanation:

Step1: Find the adjacent - interior angle to 100°.

The adjacent - interior angle to the 100° exterior angle and the 100° angle are supplementary. Let the adjacent - interior angle be $y$. Then $y + 100^{\circ}=180^{\circ}$, so $y = 180^{\circ}-100^{\circ}=80^{\circ}$.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is 180°. In the triangle, we know two angles: one is 38° and the other is $y = 80^{\circ}$. Let the third angle be $x$. Then $x+38^{\circ}+80^{\circ}=180^{\circ}$.

Step3: Solve for $x$.

$x=180^{\circ}-(38^{\circ}+80^{\circ})=180^{\circ}-118^{\circ}=62^{\circ}$.

Answer:

A. 62°