Question

question 3

1. what is measure of angle psq?

your answer

Explanation:

Step1: Set up equation based on angle - sum

The sum of the angles \(2x^{\circ}\) and \((9x - 6)^{\circ}\) is equal to \(71^{\circ}\). So, \(2x+(9x - 6)=71\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+9x-6 = 11x-6\). So the equation becomes \(11x - 6=71\).

Step3: Solve for \(x\)

Add 6 to both sides: \(11x=71 + 6=77\). Then divide both sides by 11: \(x=\frac{77}{11}=7\).

Step4: Find measure of \(\angle PSQ\)

\(\angle PSQ=(9x - 6)^{\circ}\). Substitute \(x = 7\) into the expression: \(9\times7-6=63 - 6=57^{\circ}\).

Answer:

\(57^{\circ}\)