Question

∠1 and ∠2 are complementary angles. if m∠1=(2x + 28)° and m∠2=(x - 19)°, 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 \(m\angle2=(x - 19)^{\circ}\) into the equation:
\((2x + 28)+(x - 19)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+x+28 - 19=90\), which simplifies to \(3x + 9=90\).

Step3: Solve for \(x\)

Subtract \(9\) from both sides: \(3x=90 - 9\), so \(3x=81\).
Divide both sides by \(3\): \(x=\frac{81}{3}=27\).

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

Substitute \(x = 27\) into \(m\angle1=(2x + 28)^{\circ}\).
\(m\angle1=2\times27+28\)
\(m\angle1=54 + 28\)
\(m\angle1 = 82^{\circ}\)

Answer:

\(82^{\circ}\)