Question

question 5

1. what is the measure of angle psq?

your answer

Explanation:

Step1: Use angle - sum property

Since $\angle PSQ+\angle QSR = 90^{\circ}$ (right - angle), we have the equation $(2x + 9)+7x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $2x+7x + 9=90$, or $9x+9 = 90$.

Step3: Isolate the variable term

Subtract 9 from both sides: $9x+9−9=90 - 9$, so $9x=81$.

Step4: Solve for x

Divide both sides by 9: $\frac{9x}{9}=\frac{81}{9}$, so $x = 9$.

Step5: Find the measure of $\angle PSQ$

Substitute $x = 9$ into the expression for $\angle PSQ$ which is $2x + 9$. Then $2\times9+9=18 + 9=27^{\circ}$.

Answer:

$27^{\circ}$