Question

∠1 and ∠2 are complementary angles. if ( m angle 1 = ( 4 x + 30 ) ^ { circ } ) and ( m angle 2 = ( x - 5 ) ^ { circ } ), then find the measure of ∠2.

Explanation:

Step1: Set up the equation

Since \(\angle1\) and \(\angle2\) are complementary, \(m\angle1 + m\angle2=90^{\circ}\).
Substitute \(m\angle1=(4x + 30)^{\circ}\) and \(m\angle2=(x - 5)^{\circ}\) into the equation:
\((4x + 30)+(x - 5)=90\)

Step2: Simplify the left - hand side

Combine like terms: \(4x+x+30 - 5=90\), which gives \(5x+25 = 90\)

Step3: Solve for \(x\)

Subtract 25 from both sides: \(5x=90 - 25\), so \(5x=65\).
Divide both sides by 5: \(x=\frac{65}{5}=13\)

Step4: Find \(m\angle2\)

Substitute \(x = 13\) into \(m\angle2=(x - 5)^{\circ}\): \(m\angle2=(13 - 5)^{\circ}=8^{\circ}\)

Answer:

\(8^{\circ}\)