Question

N ∆GHI, HI = GH, m∠H = 4x + 4, and m∠G = 2x + 24. What is m∠I?

Answer 1

∠I = 63.2°

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°