Question

the angles shown are complementary angles. determine the measures of ∠1 and ∠2. what are the measures of ∠1 and ∠2? m∠1 = (simplify your answer) m∠2 = (simplify your answer)

Explanation:

Step1: Use complementary - angle property

Since the two angles are complementary, their sum is 90 degrees. So, $x+(20x + 27)=90$.

Step2: Combine like - terms

Combining like - terms in the equation $x+(20x + 27)=90$, we get $21x+27 = 90$.

Step3: Solve for x

Subtract 27 from both sides: $21x=90 - 27=63$. Then divide both sides by 21, so $x = \frac{63}{21}=3$.

Step4: Find measure of ∠1

Substitute $x = 3$ into the expression for ∠1. $m\angle1=20x + 27=20\times3+27=60 + 27=87^{\circ}$.

Step5: Find measure of ∠2

Substitute $x = 3$ into the expression for ∠2. $m\angle2=x = 3^{\circ}$.

Answer:

$m\angle1 = 87^{\circ}$
$m\angle2 = 3^{\circ}$