Question

In Δghi, the line segment from g to i is extended through point i to point j. Given that measure of ∠hij = (9x - 15)°, measure of ∠igh = (3x + 13)°, and measure of ∠ghi = (3x + 8)°, find measure of ∠igh.

Answer 1

To find the measure of ∠IGH, we can use the fact that the angles in a triangle add up to 180 degrees. We can set up an equation and solve for x, then substitute the value of x to find the measure of ∠IGH.

Step-by-step explanation:

To find the measure of ∠IGH, we can use the fact that the angles in a triangle add up to 180 degrees. Since the angle measures are given in terms of x, we can set up an equation and solve for x. Then, we can substitute the value of x back into the equation for ∠IGH to find its measure.

Given: ∠HIJ = (9x - 15)°, ∠IGH = (3x + 13)°, ∠GHI = (3x + 8)°

Since the sum of the angles in a triangle is 180 degrees, we have:

(9x - 15) + (3x + 13) + (3x + 8) = 180

Simplifying the equation, we get:

15x + 6 = 180

Subtracting 6 from both sides, we have:

15x = 174

Dividing both sides by 15, we find:

x = 11.6

Substituting x = 11.6 back into the equation for ∠IGH, we get:

∠IGH = (3 * 11.6 + 13)° = 49.8°

Learn more about Triangle angles