Question

for each part below, use the figure to fill in the blank. if necessary, you may learn what the markings on a figure indicate. (a) find ( mangle q ). (b) find ( mangle m ). ( mangle q = square^circ ) ( mangle m = square^circ )

Explanation:

Step1: Identify triangle type (a)

Triangle QRS is isosceles, $RQ=RS=9$, so $\angle Q = \angle S$.

Step2: Calculate $\angle Q$ (a)

Sum of angles in triangle is $180^\circ$. Let $m\angle Q = x$.
$$x + x + 50^\circ = 180^\circ$$
$$2x = 180^\circ - 50^\circ = 130^\circ$$
$$x = \frac{130^\circ}{2} = 65^\circ$$

Step3: Identify triangle type (b)

Triangle PNM is equilateral, all sides marked equal, so all angles are equal.

Step4: Calculate $\angle M$ (b)

Sum of angles in triangle is $180^\circ$.
$$m\angle M = \frac{180^\circ}{3} = 60^\circ$$

Answer:

(a) $m\angle Q = 65^\circ$
(b) $m\angle M = 60^\circ$