Question

Please provide an answer

Answer 1

14z-7=112degree
10z=85 degree
8z=68 degree

Answer 2

`<D=95`

Explanation:

The opposite angles in a quadrilateral theorem states that when a quadrilateral is inscribed in a circle, the angles that are opposite each other are supplementary, their degree measures add up to 180 degrees. One can apply this here by using the sum of (<C) and (<A) to find the measure of the parameter (z). Then one can substitute in the value of (z) to find the measure of (<B). Finally, one can use the opposite angles in a quadrilateral theorem to find the measure of angle (<D) by using the sum of (<B) and (D).

Use the opposite angles in an inscribed quadrialteral theorem,

<A + <C = 180

Substitute,

14x - 7 + 8z = 180

Simplify,

22z - 7 = 180

Inverse operations,

22z = 187

z =
`(187)/(22)`

Simplify,

z =
`(17)/(2)`

Now substitute the value of (z) into the expression given for the measure of angle (<B)

<B = 10z

<B = 10(
`(17)/(2)`)

Simplify,

<B = 85

Use the opposite angles in an inscribed quadrilateral theorem to find the measure of (<D)

<B + <D = 180

Substitute,

85 + <D = 180

Inverse operations,

<D = 95