Question

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

Answer 1

Answer:

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°

Answer 2

Answer: $\angle G=23\°$

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:

$Inscribed\ Angle=\frac{Intercepted\ Arc}{2}$

You know that:

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

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

$(x+2)=\frac{(6x -80)}{2}\\\\2(x+2)=6x-80\\\\2x+4=6x-80\\\\4+80=6x-2x\\\\84=4x\\\\x=\frac{84}{4}\\\\x=21$

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

 $\angle G=(21 + 2)\°=23\°$