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Angle Sum Property

In □ PQRS , m...

Question

In □PQRS, m∠P = 70°, m∠Q = 115° and m∠R = 75°. What is the measure of ∠S?

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Solution

We know that the sum of the angles of a quadrilateral is 360°
∴ In $□$ PQRS,
m $∠$ P + m $∠$ Q + m $∠$ R + m $∠$ S = 360°
⇒ 70° + 115° + 75° + m $∠$ S = 360°
⇒ (70° + 115° + 75°) + m $∠$ S = 360°
⇒ 260° + m $∠$ S = 360°
⇒ m $∠$ S = 360° – 260°
⇒ m $∠$ S = 100°

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∠ P = 70^{\circ}

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