quadrilateral abcd is inscribed in a circle. m∠a is 64°, m∠b is (6x + 4)°, and m∠c is (9x - 1)°. what is…

Explanation:

Step1: Use property of cyclic quadrilateral

In a cyclic quadrilateral, opposite - angles are supplementary, i.e., $\angle A+\angle C = 180^{\circ}$ and $\angle B+\angle D=180^{\circ}$. First, find the value of $x$ using $\angle A+\angle C = 180^{\circ}$. $64+(9x - 1)=180$

Step2: Solve for $x$

$64 + 9x-1=180$ $9x+63 = 180$ $9x=180 - 63$ $9x=117$ $x = 13$

Step3: Find $\angle B$

Substitute $x = 13$ into the expression for $\angle B$. $\angle B=(6x + 4)^{\circ}=(6\times13 + 4)^{\circ}=(78 + 4)^{\circ}=82^{\circ}$

Step4: Find $\angle D$

Since $\angle B+\angle D = 180^{\circ}$ in a cyclic quadrilateral. $\angle D=180-\angle B$ $\angle D=180 - 82=98^{\circ}$

Answer:

D. $98^{\circ}$