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 ( m angle q ).
(b) find ( m angle m ).
( m angle q=square^{circ} )
( m angle m=square^{circ} )

Explanation:

Part (a)

Step1: Identify triangle type

Triangle \( QRS \) has \( QR = RS = 5 \), so it's isosceles with \( \angle Q=\angle S \).

Step2: Sum of angles in triangle

Sum of angles in a triangle is \( 180^\circ \). Let \( \angle Q = \angle S = x \). Then \( 80^\circ + x + x = 180^\circ \).

Step3: Solve for \( x \)

\( 2x = 180^\circ - 80^\circ = 100^\circ \), so \( x=\frac{100^\circ}{2}=50^\circ \).

Step1: Identify triangle type

Triangle \( PMN \) has all sides marked equal (isosceles? No, all sides equal, so equilateral). In an equilateral triangle, all angles are \( 60^\circ \).

Step2: Conclude angle measure

Since \( \triangle PMN \) is equilateral, \( \angle M = 60^\circ \).

Answer:

\( 50 \)

Part (b)