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