ABCD is a cyclic quadrilateral such that when sides AB and DC are produced, they meet at E, and sides AD and BC meet at F, when produced. If ∠ADE = 80° and ∠AED = 50°, then what is the measures of ∠ AFB
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 30°
∠ADC + ∠ABC = 180° (Sum of opposite angle of a cyclic quadrilateral will be equal to 180)
∠ABC = 180 - 80 = 100°.
In triangle AED,
∠ADE + ∠DEA + ∠DAE = 180°
80 + 50 + ∠DAE = 180
∠DAE = 50°.
Now in triangle ABF,
∠AFB = 180 - ∠ABF - ∠BAF
= 180 - 100 - 50
= 30°.