Question

In quadrilateral AGHI, where segment HI is equal to segment GH, the measure of angle IHG is represented as 3x + 4, while the measure of angle IGH is 2x - 24. What is the measurement of angle HIG?

A) 28
B) 20
C) 32
D) 40

Answer 1

The measurement of angle HIG in quadrilateral AGHI is 124 degrees.

Step-by-step explanation:

To find the measurement of angle HIG, we need to consider that the sum of the angles in a quadrilateral is always 360 degrees. We know that angle IHG is represented as 3x + 4, and angle IGH is represented as 2x - 24. Since segment HI is equal to segment GH, angle IHG and angle IGH are congruent. Therefore, we can set up the following equation:

(3x + 4) + (2x - 24) + (2x - 24) + (3x + 4) = 360

Simplifying the equation:

10x - 40 = 360

10x = 400

x = 40

Substituting x back into the expressions for angle IHG and angle IGH:

Angle IHG = 3x + 4 = 3(40) + 4 = 124 degrees

Angle IGH = 2x - 24 = 2(40) - 24 = 56 degrees

Since angle HIG is congruent to angle IHG and angle IGH, its measurement is also 124 degrees. Therefore, the correct answer is D) 40.