Question

use the figure shown. what is the value of y? a 83 b 89 c 96 d 97

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the left - hand triangle, we can find the third angle. Let the third angle of the left - hand triangle be $z$. Then $z=180-(46 + 51)$.
$z=180 - 97=83^{\circ}$.

Step2: Use vertical angles property

The angle $y$ and the angle $z$ are vertical angles. Vertical angles are equal. So $y = z$. Since $z = 83^{\circ}$, then $y=83^{\circ}$.

Answer:

A. 83