Question

find the measure of the missing angles. answer attempt 1 out of 2 x = y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle vertical to the $30^{\circ}$ angle is also $30^{\circ}$. And $x$ and the $30^{\circ}$ angle are complementary (since the two lines are perpendicular and form a right - angle of $90^{\circ}$).
$x + 30^{\circ}=90^{\circ}$

Step2: Solve for $x$

Subtract $30^{\circ}$ from both sides of the equation $x + 30^{\circ}=90^{\circ}$.
$x=90^{\circ}-30^{\circ}=60^{\circ}$

Step3: Use linear - pair property

$x$ and $y$ form a linear pair, so $x + y=180^{\circ}-90^{\circ}=90^{\circ}$ (because the two perpendicular lines divide the straight - line into two right - angles). Since $x = 60^{\circ}$, then $y=90^{\circ}-x$.
$y=90^{\circ}-60^{\circ}=30^{\circ}$

Answer:

$x = 60$, $y = 30$