Answer:
x = 15
∠H = 82
∠I = 49
∠G = 49
Explanation:
Note that side HG and side HI are congruent ( indicated by the little dashed line ) which means that their opposite angles are congruent ( ∠I and ∠G to be more specific. )
Angles in a triangle add up to equal 180°
Hence, 3x + 37 + 2 ( 4x - 11 ) = 180 ( note that the 2 in 2(4x - 11) came from angles I and G being congruent )
We now solve for x
3x + 37 + 2 ( 4x - 11 ) = 180
step 1 distribute the 2 to the 4x and -11
2 + 4x = 8x
-11 * 2 = -22
we now have 3x + 37 + 8x -22 = 180
step 2 combine like temrs
3x + 8x = 11x
37 - 22 = 15
we now have 11x + 15 = 180
step 3 subtract 15 from each side
15 - 15 cancels out
180 - 15 = 165
we now have 11x = 165
step 4 divide each side by 11
11x / 11 = x
165 / 11 = 15
we're left with x = 15
Our final step is to find the measures of ∠G, ∠H and ∠I
We can do this by simply replacing x with 15 in their given expression
∠H = 3x + 37
* substitute 15 with x *
3 ( 15 ) + 37
3 * 15 = 45
45 + 37 = 82
Hence, ∠H = 82
∠I = 4x - 11
* substitute x with 15 *
4(15) - 11
4 * 15 = 60
60 - 11 = 49
Hence, ∠I = 49
Like stated previously ∠G and ∠I are congruent
Hence, ∠G = 49