Question

∠1 and ∠2 are supplementary angles. if (mangle1=(2x + 16)^{circ}) and (mangle2=(6x - 20)^{circ}), then find the measure of ∠1. answer attempt 1 out of 2

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(2x + 16)^{\circ}\) and \(m\angle2=(6x - 20)^{\circ}\) into the equation: \((2x + 16)+(6x - 20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+6x+16 - 20 = 180\), which gives \(8x-4 = 180\).

Step3: Solve for \(x\)

Add 4 to both sides of the equation: \(8x-4 + 4=180 + 4\), so \(8x=184\).
Divide both sides by 8: \(x=\frac{184}{8}=23\).

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

Substitute \(x = 23\) into the expression for \(m\angle1\): \(m\angle1=(2x + 16)^{\circ}\).
\(m\angle1=2\times23+16\).
\(m\angle1 = 46+16\).
\(m\angle1=62^{\circ}\).

Answer:

\(62^{\circ}\)