Question

∠1 and ∠2 are complementary angles. if m∠1=(2x−28)° and m∠2=(x−8)°, then find the measure of ∠1.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(2x - 28)^{\circ}\) and \(m\angle2=(x - 8)^{\circ}\) into the equation: \((2x-28)+(x - 8)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+x-28 - 8=90\), which simplifies to \(3x-36 = 90\).

Step3: Solve for \(x\)

Add \(36\) to both sides: \(3x-36 + 36=90 + 36\), so \(3x=126\).
Divide both sides by \(3\): \(x=\frac{126}{3}=42\).

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

Substitute \(x = 42\) into \(m\angle1=(2x - 28)^{\circ}\).
\(m\angle1=2\times42-28\).
First, calculate \(2\times42 = 84\), then \(84-28=56\).

Answer:

\(56^{\circ}\)