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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°

20%

step-by-step explanation: