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 - 15)°. what is the value of x? express your answer in decimal form rounded to the nearest tenth.

Explanation:

Step1: Use angle - addition property

Since $\angle RTY=\angle RTW+\angle WTY$, we can set up the equation $5x - 15=36+(3x + 6)$.

Step2: Simplify the right - hand side

First, simplify the right - hand side of the equation: $36+(3x + 6)=3x+36 + 6=3x + 42$. So the equation becomes $5x-15 = 3x+42$.

Step3: Move the $x$ terms to one side

Subtract $3x$ from both sides: $5x-3x-15=3x-3x + 42$, which simplifies to $2x-15 = 42$.

Step4: Isolate the $x$ term

Add 15 to both sides: $2x-15 + 15=42+15$, so $2x=57$.

Step5: Solve for $x$

Divide both sides by 2: $x=\frac{57}{2}=28.5$.

Answer:

$28.5$