Question

if m∠p is six less than twice the measure of ∠q, and ∠p and ∠q are supplementary, find each angle measure.

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles add up to 180 degrees. Let \(m\angle Q=x\). Then \(m\angle P = 2x - 6\).

Step2: Set up an equation

Since \(\angle P\) and \(\angle Q\) are supplementary, we have the equation \(m\angle P+m\angle Q=180\), so \((2x - 6)+x=180\).

Step3: Combine like - terms

Combining the \(x\) terms on the left - hand side gives \(3x-6 = 180\).

Step4: Add 6 to both sides

Adding 6 to both sides of the equation: \(3x-6 + 6=180 + 6\), which simplifies to \(3x=186\).

Step5: Solve for \(x\)

Dividing both sides by 3: \(x=\frac{186}{3}=62\).

Step6: Find the measure of \(\angle P\) and \(\angle Q\)

\(m\angle Q=x = 62^{\circ}\).
\(m\angle P=2x - 6=2\times62-6=124 - 6=118^{\circ}\).

Answer:

\(m\angle P = 118^{\circ}\), \(m\angle Q=62^{\circ}\)