Question

∠1 and ∠2 are supplementary angles. if ( m angle 1 = ( 7 x + 9 ) ^ { circ } ) and ( m angle 2 = ( 3 x + 11 ) ^ { circ } ), then find the measure of ∠2.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(7x + 9)^{\circ}\) and \(m\angle2=(3x + 11)^{\circ}\) into the equation:
\((7x + 9)+(3x + 11)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(7x+3x + 9+11=180\)
\(10x+20 = 180\)

Step3: Solve for \(x\)

Subtract \(20\) from both sides:
\(10x=180 - 20\)
\(10x=160\)
Divide both sides by \(10\):
\(x=\frac{160}{10}=16\)

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

Substitute \(x = 16\) into \(m\angle2=(3x + 11)^{\circ}\)
\(m\angle2=(3\times16+11)^{\circ}\)
\(m\angle2=(48 + 11)^{\circ}\)
\(m\angle2=59^{\circ}\)

Answer:

\(59^{\circ}\)