Question 108

ABCD is a cyclic quadrilateral, AB is the diameter of the circle. If $$\angle$$ACD = 50$$^\circ$$, the measure of $$\angle$$BAD is

Solution

Given,  $$\angle$$ACD = 50$$^\circ$$

Angle subtended by the diameter in a semicircle is 90$$^\circ$$

$$=$$>  $$\angle$$ACB = 90$$^\circ$$

In cyclic quadrilateral ABCD, sum of opposite angles = 180$$^\circ$$

$$=$$>  $$\angle$$BAD + $$\angle$$BCD = 180$$^\circ$$

$$=$$>  $$\angle$$BAD + $$\angle$$ACB + $$\angle$$ACD = 180$$^\circ$$

$$=$$>  $$\angle$$BAD + 90$$^\circ$$ + 50$$^\circ$$ = 180$$^\circ$$

$$=$$>  $$\angle$$BAD + 140$$^\circ$$ = 180$$^\circ$$

$$=$$>  $$\angle$$BAD = 40$$^\circ$$

Hence, the correct answer is Option B


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