Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (5x - 11)^\circ$ and $m\angle 2 = (5x - 19)^\circ$, then find the measure of $\angle 2$.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(5x - 11)^{\circ}\) and \(m\angle2=(5x - 19)^{\circ}\) into the equation:
\((5x - 11)+(5x - 19)=90\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(5x+5x-11 - 19=90\)
\(10x-30 = 90\)

Step3: Solve for \(x\)

Add \(30\) to both sides of the equation:
\(10x-30 + 30=90 + 30\)
\(10x=120\)
Divide both sides by \(10\):
\(x=\frac{120}{10}=12\)

Step4: Find the measure of \(\angle2\)

Substitute \(x = 12\) into \(m\angle2=(5x - 19)^{\circ}\)
\(m\angle2=(5\times12-19)^{\circ}\)
\(m\angle2=(60 - 19)^{\circ}\)
\(m\angle2 = 41^{\circ}\)

Answer:

\(41^{\circ}\)