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

Answer:

$84^{\circ}$

Step-by-step 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 $9x+21$:

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

Answer 2

Answer:

-31

Step-by-step explanation: