If the measure of arc ad = (6x -80)° and < g = (x + 2)°, what is the measure of < g?

Step-by-step 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:

You know that:

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

Substituting the value of "x" into you get:

The measure of <G =  23°

Step-by-step 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°

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