Question

what is m∠q? m∠q =

Explanation:

Step1: Recall angle - sum property in a semi - circle

The triangle $\triangle PQR$ is inscribed in a semi - circle, so $\angle R = 90^{\circ}$. In a triangle, the sum of interior angles is $180^{\circ}$. So, $(5x + 12)+(2x + 22)+90=180$.

Step2: Simplify the equation

Combine like terms: $5x+2x+12 + 22+90=180$, which gives $7x+124 = 180$.

Step3: Solve for $x$

Subtract 124 from both sides: $7x=180 - 124$, so $7x = 56$. Then divide both sides by 7: $x=\frac{56}{7}=8$.

Step4: Find $m\angle Q$

Substitute $x = 8$ into the expression for $\angle Q$. $m\angle Q=5x + 12$. So, $m\angle Q=5\times8+12=40 + 12=52^{\circ}$.

Answer:

$52$