Question

given that m∠y = 45°, find m∠a and m∠b. m∠a = m∠b =

Explanation:

Step1: Use complementary - angle property

Since $\angle y$ and $\angle a$ are complementary (the two angles add up to 90° as the vertical - horizontal lines are perpendicular), we have $m\angle a=90^{\circ}-m\angle y$.
$m\angle a = 90 - 45$

Step2: Use supplementary - angle property

Since $\angle b$ and $\angle y$ are supplementary (the two angles form a straight - line, and the sum of angles on a straight - line is 180°), we have $m\angle b=180^{\circ}-m\angle y$.
$m\angle b = 180 - 45$

Answer:

$m\angle a = 45$
$m\angle b = 135$