Question

question ∠1 and ∠2 are supplementary angles. if m∠1 = (2x − 11)° and m∠2 = (8x + 21)°, then find the measure of ∠1. answer attempt 1 out of 2 submit answer watch video show examples

Explanation:

Step1: Set up the equation for supplementary angles

Since ∠1 and ∠2 are supplementary, their measures add up to \(180^\circ\). So, \((2x - 11) + (8x + 21) = 180\).

Step2: Combine like terms

Simplify the left - hand side: \(2x+8x-11 + 21=180\), which becomes \(10x + 10=180\).

Step3: Solve for x

Subtract 10 from both sides: \(10x=180 - 10=170\). Then divide both sides by 10: \(x=\frac{170}{10} = 17\).

Step4: Find the measure of ∠1

Substitute \(x = 17\) into the expression for \(m\angle1\): \(m\angle1=(2\times17-11)^\circ=(34 - 11)^\circ = 23^\circ\).

Answer:

\(23^\circ\)