Question

ABCD is a cyclic trapezium with AD || BC. If ∠B = 70°, determine other three angles of the trapezium.

Answer 1

If in cyclic quadrilateral `angle B = 70°` , then we have to find the other three angles. 

Since, AD is parallel to BC, So,
 `angleB + angleA = 180 ` (Alternate interior angles)

`70 + angleA = 180`

`⇒ angle A = 180 - 70 = 110°`

Now, since ABCD is cyclic quadrilateral, so

`angle A + angle C = 180`

`⇒ 110 + angle C = 180`

`⇒ angle C = 180 - 110 = 70°`

And,

`angle B + angleD = 180`\

`⇒ 70 + angleD = 180`

`⇒ angleD = 180 - 70 = 110°`

\[Hence, \angle A = 110°, \angle C = 70° \text{ and }  \angle D = 110°\]