Answer:
a) x = 9, m∠FGH = 30°
b) m∠HGI = 30°
c) m∠FGI = 60°
Explanation:
In geometry, when we say that a line or ray bisects an angle, it means that the line or ray divides the angle into two congruent angles. In other words, it splits the angle into two smaller angles of equal measure.
If ray GH bisects ∠FGI then ∠HGI ≅ ∠FGH.
From observation of the given diagram:
- m∠HGI = (5x - 15)°
- m∠FGH = (4x - 6)°
To find x, set the angles equal to each other and solve for x:
m∠HGI = m∠FGH
(5x - 15)° = (4x - 6)°
5x - 15 = 4x - 6
x = 9
To find the measure of ∠FGH, substitute the found value of x into the expression for ∠FGH:
m∠FGH = (4x - 6)°
m∠FGH = (4(9) - 6)°
m∠FGH = (36 - 6)°
m∠FGH = 30°
Since ∠HGI ≅ ∠FGH, and m∠FGH = 30°, then m∠HGI = 30°.
From observation of the given diagram, ∠FGI is the sum of ∠HGI and ∠FGH. As ∠HGI ≅ ∠GFH, then:
m∠FGI = 2 × m∠HGI
m∠FGI = 2 × 30°
m∠FGI = 60°