Question

(c) problem 16: find x, y, and z. after you enter your answer press go. x = y = z =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So $x = 58$ since the angle marked $x^{\circ}$ and the $58^{\circ}$ angle are vertical angles.

Step2: Find $y$ using angle - sum property

In the left - hand triangle, we know one angle is $62^{\circ}$ and another is $x = 58^{\circ}$. The sum of angles in a triangle is $180^{\circ}$. Let's find the third angle which is $2y^{\circ}$.
$180-(62 + 58)=2y$
$180 - 120=2y$
$60 = 2y$
$y = 30$

Step3: Find $z$ using angle - sum property

In the left - hand triangle, we know two angles are $62^{\circ}$ and $58^{\circ}$. Using the angle - sum property of a triangle ($180^{\circ}$ for the sum of interior angles of a triangle), we have $z+62 + 58=180$.
$z=180-(62 + 58)$
$z = 60$

Answer:

$x = 58$, $y = 31$, $z = 60$