Question

In a quadrilateral ABCD, side AD is parallel to side BC. If Angle A: Angle B= 2:3 and Angle C: Angle D =4:5, find each angle of the quadrilateral ABCD.
please help
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Answer 1

∠A:∠D=2:3

Let ∠A and ∠D be 2x and 3x.

⇒ ∠B:∠C=7:8

Let ∠A and ∠D be 7y and 8y.

Since, AB∥CD and AD is a transversal.

∴ ∠A+∠D=180°

. [ Interior angles on same side of transversal ]

⇒ 2x+3x=180°

.

⇒ 5x=180°

.

⇒ x=36°

⇒ ∠A=2×36° =72°

⇒ ∠D=3×36° =108°

.

Since, AB∥CD and BC is a transversal.

∴ ∠B+∠C=180°

. [ Interior angles on same side of transversal ]

⇒ 7y+8y=180°

⇒ 15y=180°

∴ y=12°

⇒ ∠B=7×12° =84°

⇒ ∠C=8×12° =96°

your answer ....

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