Answer:
∠I = 63.2°
Step-by-step explanation:
Here, In ∆GHI , HI = GH,
∠H = (4x + 4), and ∠G = (2x + 24)
Now, by the Result: Angles opposite to equals sides are equal.
So, if H I = G H
⇒∠I = ∠H = ( 4x + 4)
Now, by ANGLE SUM PROPERTY in ∆GHI, :
∠I + ∠H + ∠G = 180°
⇒( 4x + 4) + ( 4x + 4) + (2x + 24) = 180°
or, 10 x + 32 = 180
or, 10 x = 180 - 32 = 148
⇒ x = 148/10 = 14.8 or, x = 14.8
Now, ∠I = ( 4x + 4) =(4 x (14.8) +4) = 63.2
or, ∠I = 63.2°
