Question

Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x − 1)°. What is m∠D? 64° 82° 90° 98° 116° NextReset

Answer 1

for an inscribed quadrilateral, the opposite angles are supplementary,
m∠A+m∠C=180
64+(9x-1)=180
9x+63=180
9x=117
x=13
m∠B=6x+4=6*13+4=82
so m∠D=180-82=98
the answer is 98.

Answer 2

m∠D is 98°

Explanation:

Given quadrilateral ABCD is inscribed in a circle.

m∠A=64°, m∠B=(6x + 4)°, and m∠C=(9x − 1)°.

we have to find the m∠D.

As, the sum of opposite angles of cyclic quadrilateral is 180 i.e they are supplementary.

∴ m∠A+m∠C=180°

64°+(9x-1)°=180°

9x+63=180

9x=117 ⇒ x=13

⇒ m∠B=6x+4=6(13)+4=82

Also, m∠B+m∠D=180°

so m∠D=180-82=98°

Hence, m∠D is 98°