Question

ABCD is a trapezium such that AB || DC,
<A: <D = 3:1, <B : <C = 5: 7. Find the
angles of the trapezium.​

Answer 1

Answer:

Given,

∠A:∠D=2:1 and ∠B:∠C=7:5

Let

∠A and ∠B be 2x and x and

∠C and ∠D be 7y and 5y

From the figure,

∠A+∠D=180

∘

(Alternate angles are supplementary)

⇒2x+x=180

∘

⇒3x=180

∘

⇒x=

3

180

∘

=60

∘

And,

∠B+∠C=180

∘

(Alternate angles are supplementary)

⇒7y+5y=180

∘

⇒12y=180

∘

⇒y=

12

18

∘

=15

∘

Hence,

∠A=2x=2×60

∘

=120

∘

∠D=x=60

∘

∠B=7y=7×15

∘

=105

∘

and

∠C=5y=5×15

∘

=75

∘