Question

GEOMETRY

1.) find the value of z and show work

a) Explain the difference in how an inscribed angle and central angle are draw

b) Explain the difference in how their measures compare to the subtended arc.

Answer 1

The value of z is 8.5

What is the value of z?

b.

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

118° = 2(6x+8)°

118 = 12x + 16

118 - 16 = 12x

102 = 12x

x = 102/12

x = 8.5

Hence,

a.

The difference in how an inscribed angle and central angle are drawn;

Let O be the center of the circle, and A, B, C are three points on the circle.

Draw OA and OC as shown in the figure. To make the central angle.

Answer 2

z = 8.5

Explanation:

Let O be the center of the circle, and A, B, C are three points on the circle.

Draw OA and OC are shown in the figure. To make the central angle.

In the figure the measure of arc AC is 118 degrees. measure of central angle and subtrahend arc is same. So, central angle is

`\angle AOC=118^(\circ)`

Subtended angle on arc AC is

`\angle ABC=(6z+8)^(\circ)`

According to central angle theorem of circle, central angle is twice of angle subtended by the arc.

`\angle AOC=2* \angle ABC`

`118^(\circ)=2* (6z+8)^(\circ)`

`118=12z+16`

`118-16=12z`

`102=12z`

`(102)/(12)=z`

`8.5=z`

Therefore, the value of z is 8.5.