Question

use the figure shown. what is the value of x? a. 38 b. 59 c. 83 d. 96

Explanation:

Step1: Find the value of $y$.

The sum of angles in a triangle is $180^{\circ}$. In the left - hand triangle, we have $y = 180-(46 + 51)$.
$y=180 - 97=83^{\circ}$

Step2: Find the value of $x$.

In the right - hand triangle, using the angle - sum property of a triangle again. Since the vertical angles are equal, the non - $x$ and non - $38^{\circ}$ angle is $y = 83^{\circ}$. So $x=180-(38 + 83)$.
$x = 59^{\circ}$

Answer:

B. 59