Answer:
m<GHI = 17°
Explanation:
m<GHI = (2x - 3)°
m<IGH = (2x + 15)°
m<HIJ = (7x - 18)°
<HIJ is an exterior angle of ∆GHI
<GHI and <HIJ are both interior angles of ∆GHI that are opposite to the exterior angle.
Therefore, based on the exterior angle theorem of a triangle, we would have the following equation:
m<GHI + m<IGH = m<HIJ
(2x - 3)° + (2x + 15)° = (7x - 18)° (substitution)
Solve for x
2x - 3 + 2x + 15 = 7x - 18
Add like terms
4x + 12 = 7x - 18
4x - 7x = -12 - 18
-3x = -30
Divide both sides by -3
x = 10
✔️m<GHI = (2x - 3)°
Plug in the value of x
m<GHI = 2(10) - 3 = 20 - 3
m<GHI = 17°