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Properties of Trapezium

and m ∠ C=105...

Question

In the figure, m∠B = 85° and m∠C = 105°. Find the measures of ∠A and ∠D.

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Solution

m∠B = 85°
But m∠B+ m∠D = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ m∠D = 180° – 85°
⇒ m∠D = 95°
∴ The measure of ∠D = 95°
m∠A =105°
But m∠A+ m∠C = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°)
⇒ m∠C = 180° –105°
⇒m∠C = 75°
∴ The measure of ∠C = 75°.

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