Answer:
m∠Q = 35°
m∠M = 60°
Step-by-step explanation:
In the isosceles triangle, the measures of the base angles are equal
In Δ RQS
∵ RQ = RS
→ That means Δ RQS is an isosceles triangle
∴ Δ RQS is an isosceles triangle
∵ ∠Q and ∠S are the base angles
∴ m∠Q = m∠S
→ The sum of the measures of the interior angles in any Δ is 180°
∴ m∠Q + m∠S + m∠R = 180°
∵ m∠R = 110°
∴ m∠Q + m∠S + 110 = 180
→ Subtract 110 from both sides
∴ m∠Q + m∠S = 70°
∵ m∠Q = m∠S
→ Divide their sum by 2 to find the measure of each one
∴ m∠Q = m∠S = 70 ÷ 2 = 35°
∴ m∠Q = 35°
In Δ MNP
∵ MN = NP = PM
→ That means ΔMNP is an equilateral triangle
∴ Δ MNP is an equilateral triangle
→ In the equilateral triangle, all angles are equal in measures
∴ m∠M = m∠N = m∠P
∵ m∠M + m∠N + m∠P = 180
→ Divide their sum by 180 to find the measure of each angle
∴ m∠M = m∠N = m∠P = 180 ÷ 3 = 60°
∴ m∠M = 60°
