Question

1. consider the diagram below. 3a first, solve for x.

Explanation:

Step1: Find angle y

Use the angle - sum property of a triangle (the sum of interior angles of a triangle is 180°) in the smaller triangle. So, $y=180-(32 + 69)$.
$y = 180 - 101=79^{\circ}$

Step2: Find angle x

Use the angle - sum property of a triangle in the larger triangle. The three angles of the larger triangle are $x$, $78^{\circ}$, and the angle adjacent to $y$ (which is also $79^{\circ}$ since they are vertical angles). So, $x=180-(78 + 79)$.
$x=180 - 157 = 23^{\circ}$

Answer:

$x = 23^{\circ}$