N∆ghi, hi = gh, m∠h = 4x + 4, and m∠g = 2x + 24. what is m∠i?

 ∠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°

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step-by-step explanation: