Question

In the diagram, GH bisects FGI. A. Solve for x and find m FGH. B. Find m HGI. C.find m FGI. A. X=_(simplify your answer)

Answer 1

Answer:

Part A) x=9 and m∠FGH=29°

Part B) m∠HGI=29°

Part C) m∠FGI=58°

Step-by-step explanation:

Part A) Solve for x and find m∠FGH

we know that

m∠FGI=m∠FGH+m∠HGI

If GH bisects FGI

then

m∠FGH=m∠HGI

substitute the values

4x-7=5x-16

solve for x

5x-4x=16-7

x=9

m∠FGH=4x-7

m∠FGH=4(9)-7=29°

Part B) Find the measure of angle HGI

m∠HGI=5x-16

Remember that

m∠FGH=m∠HGI

Verify

m∠HGI=5(9)-16=29° -----> is correct

Part C) Find the measure of angle FGI

m∠FGI=m∠FGH+m∠HGI

substitute the values

m∠FGI=29°+29°=58°