Question

The adjacent angles of an isosceles trapezium ABCD are in the ratio 1:3. Find the
measurement of all angles.

Answer 1

Answer:

n an isosceles trapezium base angles are equal; ∠P=∠Q.

Let ∠P=x

∘

and ∠S=2x

∘

. Since ∠P+∠S=180

∘

(one pair of adjacent angles of a trapezium is supplementary), we get

x

∘

+2x

∘

=180

∘

.

Thus 3x

∘

=180

∘

or x

∘

=180

∘

/3=60

∘

. Hence ∠P=60

∘

and ∠S=2×60

∘

=120

∘

. Since ∠P=∠Q, we get ∠Q=60

∘

. But, ∠Q+∠R=180

∘

(one pair of adjacent angles are supplementary). Hence we also get ∠R=180

∘

−60

∘

=120

∘

.