Question

∠1 and ∠2 are supplementary angles. if m∠1=(7x + 21)° and m∠2=(x - 17)°, 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 \(m\angle1=(7x + 21)^{\circ}\) and \(m\angle2=(x - 17)^{\circ}\) into the equation:
\((7x + 21)+(x - 17)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+x+21 - 17=180\), which simplifies to \(8x + 4=180\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(8x=180 - 4\), so \(8x=176\).
Divide both sides by \(8\): \(x=\frac{176}{8}=22\).

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

Substitute \(x = 22\) into \(m\angle2=(x - 17)^{\circ}\).
\(m\angle2=(22-17)^{\circ}=5^{\circ}\)

Answer:

\(5^{\circ}\)