Question

in the figure below, ( m angle 1 = 4x^{circ} ) and ( m angle 2 = (x - 5)^{circ} ). find the angle measures.

Explanation:

Step1: Set up the equation

Since \(\angle1\) and \(\angle2\) are complementary (\(\angle1+\angle2 = 90^{\circ}\)), we have \(4x+(x - 5)=90\).

Step2: Simplify the equation

Combine like - terms: \(4x+x-5 = 90\), which becomes \(5x-5 = 90\).

Step3: Solve for \(x\)

Add \(5\) to both sides: \(5x=90 + 5=95\). Then divide by \(5\): \(x=\frac{95}{5}=19\).

Step4: Find \(m\angle1\)

Substitute \(x = 19\) into \(m\angle1=4x\). So \(m\angle1=4\times19 = 76^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 19\) into \(m\angle2=(x - 5)\). So \(m\angle2=19-5 = 14^{\circ}\).

Answer:

\(m\angle1 = 76^{\circ}\), \(m\angle2 = 14^{\circ}\)