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 measure of ∠AFB ?
Answer & explanation
Correct answer: option 4
From the above diagram,
= \(\angle\)ADC + \(\angle\)CDF = 180 [Linear pair of angles]
= 80 + \(\angle\)CDF = 180
= \(\angle\)CDF = 100
Now, In \(\Delta \)AED
= \(\angle\)AED + \(\angle\)ADE + \(\angle\)EAD = 180
= 50 + 80 + \(\angle\)EAD = 180
= \(\angle\)EAD = 180 - 130 = 50
Now, \(\angle\)EAD = \(\angle\)DCF = 50
In \(\Delta \)DCF
= \(\angle\)CDF + \(\angle\)DFC + \(\angle\)DCF = 180
= 100 + \(\angle\)DFC + 50 = 180
= \(\angle\)DFC = 180 - 150 = 30
= \(\angle\)DFC = \(\angle\)AFB = \({30}^\circ\)
Therefore, \(\angle\)AFB is \({30}^\circ\).