Question

∠1 and ∠2 are supplementary angles. if (mangle1=(3x + 20)^{circ}) and (mangle2=(7x - 30)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(3x + 20)^{\circ}\) and \(m\angle2=(7x - 30)^{\circ}\) into the equation: \((3x + 20)+(7x - 30)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+7x+20 - 30=180\), which simplifies to \(10x-10 = 180\).

Step3: Solve for \(x\)

Add 10 to both sides of the equation: \(10x-10 + 10=180 + 10\), getting \(10x=190\).
Divide both sides by 10: \(x=\frac{190}{10}=19\).

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

Substitute \(x = 19\) into the expression for \(m\angle2\): \(m\angle2=(7x - 30)^{\circ}\).
\(m\angle2=7\times19-30\).
\(m\angle2 = 133-30=103^{\circ}\).

Answer:

\(103^{\circ}\)