Question

∠1 and ∠2 are complementary angles. if (mangle1=(6x + 12)^{circ}) and (mangle2=(5x - 21)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Recall complementary - angle property

Complementary angles add up to 90°. So, \(m\angle1 + m\angle2=90^{\circ}\).
\((6x + 12)+(5x - 21)=90\)

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms:
\(6x+5x+12 - 21 = 90\)
\(11x-9 = 90\)

Step3: Solve for \(x\)

Add 9 to both sides of the equation:
\(11x-9 + 9=90 + 9\)
\(11x=99\)
Divide both sides by 11:
\(x=\frac{99}{11}=9\)

Step4: Find the measure of \(\angle1\)

Substitute \(x = 9\) into the expression for \(m\angle1\):
\(m\angle1=(6x + 12)^{\circ}=(6\times9 + 12)^{\circ}\)
\(=(54 + 12)^{\circ}=66^{\circ}\)

Answer:

\(66^{\circ}\)