Question

8. In a quadrilateral ABCD, it is being given that AB || DC.
angle A: angle D = 2:3 and angle B : angle C = 4:5.
Find the measure of each angle of quadrilateral ABCD.
(Hint: 2x + 3x = 180 and 4y + 5y = 180.]
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Answer 1

Answer:

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Step-by-step explanation:

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

o

. [ Interior angles on same side of transversal ]

⇒ 7y+8y=180

o

⇒ 15y=180

o

∴ y=12

o