Question

in $\triangle opq$, $mangle o=(8x + 13)^{circ}$, $mangle p=(4x - 12)^{circ}$, and $mangle q=(x + 10)^{circ}$. what is the value of $x$?

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle O+m\angle P + m\angle Q=180^{\circ}\).
\((8x + 13)+(4x-12)+(x + 10)=180\)

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms on the left - hand side.
\((8x+4x + x)+(13-12 + 10)=180\)
\(13x+11 = 180\)

Step3: Isolate the variable \(x\)

Subtract 11 from both sides of the equation.
\(13x=180 - 11\)
\(13x=169\)
Then divide both sides by 13.
\(x=\frac{169}{13}\)
\(x = 13\)

Answer:

13