Question

100 PIONTS AND BRIANLIST, HELP IN THE GIF, DO ALL PARTS

Answer 1

2x -1° = 3x - 16°

-x = -15°

x = 15°

so, m<fgh = 2*15-1 = 29° and m<hgi = 29° because they both are equal

and m<fgi = 29°*2 = 58°

Answer 2

• x = 15°
• m∠FGH = 29°
• m∠HGI = 29°
• m∠FGI = 58°

Given :

• A ray GH bisects ∠FGI

To find :

• Value of x & measure ∠FGH
• Measure ∠HGI
• Measure ∠FGI

Solution :

We know that, when a ray bisects an angle,it means it divides it into two equal parts , therefore,

• Measure ∠FGH = Measure ∠HGI
• 2x - 1° = 3x - 16°
• 2x - 3x = -16° +1°
• -x = -15°
• x = 15°

Hence, the value of x would be equal to 15°.

Plugging in the value of x in angle ∠FGI & ∠HGI

• 2x -1° = 2*15° - 1° = 29°
• 3x -16° = 3*15° - 16° = 29°

Thus, Measure ∠FGI & ∠HGI would be same i.e. 29°

And , since GH bisected ∠FGH,

Thereby,

• Measure ∠FGH + Measure ∠HGI = Measure∠FGI
• 29° + 29° = Measure∠FGI
• Measure∠FGI = 58°

Thus , Measure∠FGI = 58°