Question

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

Explanation:

Step1: Find angle $y$

In the smaller triangle, using the angle - sum property of a triangle ($180^{\circ}$ sum), we have $y=180-(32 + 69)$.
$y = 180 - 101=79^{\circ}$

Step2: Find angle $x$

In the larger triangle, using the angle - sum property of a triangle. The third angle in the larger triangle adjacent to $y$ is also $y$ (vertically opposite angles). So $x=180-(78 + 79)$.
$x=180 - 157 = 23^{\circ}$

Answer:

$x = 23^{\circ}$