Question

three angles are shown. the measure of angle rtw = 36°, the measure of angle wty=(3x + 6)°, and the measure of angle rty=(8x - 16)°. what is the value of x? express your answer in decimal form rounded to the nearest tenth.

Explanation:

Step1: Set up equation

Since $\angle RTW+\angle WTY=\angle RTY$, we have $36+(3x + 6)=8x-16$.

Step2: Simplify left - hand side

Combine like terms on the left - hand side: $36+3x + 6=3x+42$. So the equation becomes $3x + 42=8x-16$.

Step3: Move x terms to one side

Subtract $3x$ from both sides: $42=8x-3x - 16$, which simplifies to $42 = 5x-16$.

Step4: Isolate x term

Add 16 to both sides: $42 + 16=5x$, so $58 = 5x$.

Step5: Solve for x

Divide both sides by 5: $x=\frac{58}{5}=11.6$.

Answer:

$11.6$