Question

in $delta vwx$, $mangle v=(x + 8)^{circ}$, $mangle w=(5x + 9)^{circ}$, and $mangle x=(3x + 10)^{circ}$. find $mangle x$.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle V+m\angle W + m\angle X=180^{\circ}\).
Substitute the given angle - measures: \((x + 8)+(5x + 9)+(3x + 10)=180\).

Step2: Combine like - terms

\((x+5x + 3x)+(8 + 9+10)=180\).
\(9x+27 = 180\).

Step3: Solve for \(x\)

Subtract 27 from both sides: \(9x=180 - 27\).
\(9x=153\).
Divide both sides by 9: \(x=\frac{153}{9}=17\).

Step4: Find \(m\angle X\)

Substitute \(x = 17\) into the expression for \(m\angle X\).
\(m\angle X=(3x + 10)^{\circ}\).
\(m\angle X=3\times17+10\).
\(m\angle X=51 + 10=61^{\circ}\).

Answer:

\(61^{\circ}\)