Question

If the measure of arc AD = (6x -80)° and <G = (x + 2)°, what is the measure of <G?
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Answer 1

The measure of <G = 23°

Explanation:

From the figure we can write,

The measure of <G is half the the measure of arc AD

To find the value of x

We have AD = (6x - 80)° and <G = (x + 2)°

6x - 80 = 2(x + 2)

6x - 80 = 2x + 4

6x - 2x = 4 + 80

4x = 84

x = 84/4 = 21

To find the measure of <g

m<G = x + 2

= 21 + 2 = 23°

Therefore the measure of <G = 23°

Answer 2

Answer:
`\angle G=23\°`

Explanation:

Remember that an inscribed angle is defined as an angle formed by two chords and whose vertex lies on the circle.

By definition, the measure of an inscribed angle is:

`Inscribed\ Angle=(Intercepted\ Arc)/(2)`

You know that:

`Intercepted\ Arc=AD = (6x -80)\\\\Inscribed\ Angle=\angle G=(x + 2)`

Then, you need to substitute values and solve for "x":

`(x+2)=((6x -80))/(2)\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=(84)/(4)\\\\x=21`

Substituting the value of "x" into
`\angle G=(x + 2)\°` you get:

`\angle G=(21 + 2)\°=23\°`