Question

GH bisects FGI. Find the measure of HGI •15° •21° •10° •8°

Answer 1

Answer:

Option B is correct.

the measure of angle HGI is 21°

Step-by-step explanation:

By Angle bisector definition:

A line that bisects the angle into equal angle

From the given figure, we have;

$\angle FGH = (2x+1)^{\circ}$ and  $\angle HGI = (3x-9)^{\circ}$

it is given that: GH bisects ∠FGI.

then by definition:

$\angle FGH = \angle HGI$

Substitute the given values we have;

$2x+1 = 3x -9$

Add 9 to both sides we get;

$2x+10= 3x$

Subtract 2x from both sides we get;

$10= x$

or

$x= 10$

then;

$\angle HGI = 3x-9 = 3(10)-9 = 30-9 = 21^{\circ}$

Therefore, the measure of angle HGI is 21°

Answer 2

Answer:

m<HGI=21°

Step-by-step explanation:

we know that

If GH bisects m<FGI then

m<FGH=m<HGI

substitute the values

(2x+1)°=(3x-9)°

solve for x

3x-2x=1+9

x=10°

The measure of angle HGI is equal to

(3x-9)° ------> substitute the value of x

3*10-9=21°

m<HGI=21°