Question

$(y-{20}^{\circ })$ and $(y+{30}^{\circ })$ are the measures of complementary angles. Find the measure of each angle.

Answer 1

Given:

$(y-{20}^{\circ })$ and $(y+{30}^{\circ })$ are the measures of complementary angles.

We know that, if sum of two angles is ${90}^{\circ }$ then they are complementary angles.

$\Rightarrow y-{20}^{\circ }+y+{30}^{\circ }={90}^{\circ }$

$\Rightarrow 2y+{10}^{\circ }={90}^{\circ }$

$\Rightarrow 2y={90}^{\circ }-{10}^{\circ }$

$\Rightarrow 2y={80}^{\circ }$

$\Rightarrow 2y=\frac{{80}^{\circ }}{2}$

$\Rightarrow y={40}^{\circ }$

Lets substitute $y={40}^{\circ }$ in $(y-{20}^{\circ })$ and $(y+{30}^{\circ })$

$y-{20}^{\circ }={40}^{\circ }-{20}^{\circ }={20}^{\circ }$ ---(1)

$y+{30}^{\circ }={40}^{\circ }+{30}^{\circ }={70}^{\circ }$ ---(2)

Hence, the measure of the two angles are ${20}^{\circ }$ and ${70}^{\circ }$.