Question

∠1 and ∠2 are supplementary angles. if m∠1=(2x−16)° and m∠2=(x+7)°, then find the measure of ∠1. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(2x - 16)^{\circ}\) and \(m\angle2=(x + 7)^{\circ}\) into the equation:
\((2x-16)+(x + 7)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(2x-16+x + 7=180\)
\(3x-9 = 180\)

Step3: Solve for \(x\)

Add \(9\) to both sides of the equation:
\(3x-9+9=180 + 9\)
\(3x=189\)
Divide both sides by \(3\):
\(x=\frac{189}{3}=63\)

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

Substitute \(x = 63\) into \(m\angle1=(2x - 16)^{\circ}\)
\(m\angle1=(2\times63-16)^{\circ}\)
\(m\angle1=(126-16)^{\circ}\)
\(m\angle1 = 110^{\circ}\)

Answer:

\(110\)