Question

Can someone please help me with this ?? im really confused but i need to pass this test!

In the circle above, the measure of angle DHG can be represented by 7x - 7, and the measure of arc DG can be represented by 9x + 21. The measure of arc DG is ___ degrees.

Answer 1

-31

Explanation:

Answer 2

`84^(\circ)`

Explanation:

The measure of an inscribed angle is exactly half the measure of the arc it forms. Thus, we have the following equation:

`2(7x-7)=9x+21`

Solving, we get:

`2(7x-7)=9x+21,\\14x-14=9x+21,\\5x=35,\\x=7`

Plugging in
`x=7` into
`9x+21`:

`\widehat{DG}=9(7)+21,\\\widehat{DG}=63+21,\\\widehat{DG}=\boxed{84^(\circ)}`