Question

In triangle ghi, ∠g = (x + 16)°, ∠h = (x + 9)°, and ∠i = (7x + 2)°. Find m∠g.

Answer 1

After setting up an equation based on the angle sum property of a triangle and solving for x, we find that the measure of angle G in triangle GHI is 33 degrees.

Step-by-step explanation:

To find the measure of angle G (m∠g) in triangle GHI, we can use the fact that the sum of angles in a triangle is always 180 degrees. We are given ∠g = (x + 16)°, ∠h = (x + 9)°, and ∠i = (7x + 2)°.

We set up an equation using the angle sum property:

(x + 16) + (x + 9) + (7x + 2) = 180

Combine like terms:

9x + 27 = 180

Subtract 27 from both sides:

9x = 153

Divide by 9:

x = 17

Now substitute x back into the expression for ∠g:

∠g = (17 + 16)°

∠g = 33°

Therefore, the measure of angle G is 33 degrees.