Question

find the measure of the missing angles.
answer attempt 1 out of 2
$x = square ^ { circ }$ $y = square ^ { circ }$

Explanation:

Step1: Find the value of \( x \)

Use the fact that the sum of angles in a right - angled situation (where one angle is \( 90^{\circ}\) and another is \( 51^{\circ}\)): \( x+90^{\circ}+51^{\circ}=180^{\circ}\) (straight - line angle). Then \( x = 180^{\circ}-90^{\circ}-51^{\circ}\).

$$x=39^{\circ}$$

Step2: Find the value of \( y \)

Use the property of vertical angles. \( y\) and \(x + 90^{\circ}\) are related as \(y=180^{\circ}-x\) (linear pair). Since \(x = 39^{\circ}\), then \(y=180^{\circ}-39^{\circ}\) (because \(y\) and \(x\) are supplementary as they form a linear pair).

$$y = 141^{\circ}$$

Answer:

\(x = 39^{\circ}\), \(y=141^{\circ}\)