Question

find ( mangle q ).

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle q = square^circ )

Explanation:

Step1: Identify opposite, adjacent sides

For $\angle Q$, opposite side $PR=4$, adjacent side $RQ=2$.

Step2: Use tangent ratio formula

$\tan(\angle Q) = \frac{\text{opposite}}{\text{adjacent}} = \frac{4}{2}=2$

Step3: Calculate angle via arctangent

$\angle Q = \arctan(2)$
Use calculator to find $\arctan(2) \approx 63.4^\circ$

Answer:

$63.4$