The problem involves a cyclic quadrilateral and some angle properties. Here are the steps to solve it:

Step 1: In a cyclic quadrilateral, the sum of opposite angles is 180°. So, if ∠AED = 30°, then ∠BCD = 180° - 30° = 150°.

Step 2: Similarly, if ∠BFA = 60°, then ∠CDA = 180° - 60° = 120°.

Step 3: Now, ∠ABC + ∠ADC = 180° (since they are on a straight line). Substituting the value of ∠ADC from step 2, we get ∠ABC = 180° - 120° = 60°.

So, the measure of ∠ABC is 60°. However, this option is not given in the choices. There might be a mistake in the problem or the choices.

Question

The problem involves a cyclic quadrilateral and some angle properties. Here are the steps to solve it:

Step 1: In a cyclic quadrilateral, the sum of opposite angles is 180°. So, if ∠AED = 30°, then ∠BCD = 180° - 30° = 150°.

Step 2: Similarly, if ∠BFA = 60°, then ∠CDA = 180° - 60° = 120°.

Step 3: Now, ∠ABC + ∠ADC = 180° (since they are on a straight line). Substituting the value of ∠ADC from step 2, we get ∠ABC = 180° - 120° = 60°.

So, the measure of ∠ABC is 60°. However, this option is not given in the choices. There might be a mistake in the problem or the choices.

Knowee AI · Accepted Answer

The problem involves a cyclic quadrilateral and some angle properties. Here are the steps to solve it:

Step 1: In a cyclic quadrilateral, the sum of opposite angles is 180°. So, if ∠AED = 30°, then ∠BCD = 180° - 30° = 150°.

Step 2: Similarly, if ∠BFA = 60°, then ∠CDA = 180° - 60° = 120°.

Step 3: Now, ∠ABC + ∠ADC = 180° (since they are on a straight line). Substituting the value of ∠ADC from step 2, we get ∠ABC = 180° - 120° = 60°.

So, the measure of ∠ABC is 60°. However, this option is not given in the choices. There might be a mistake in the problem or the choices.

ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is:Choices:- 85° 65° 75° 90°