Question

In ΔFGH, if m∠FGH = (x - 2)°, m∠GHI = (4x - 5)°, and m∠HFG = (x + 19)°, what is the measure of ∠HFG?

A) (x - 2)°
B) (x + 19)°
C) (4x - 5)°
D) It cannot be determined with the given information.

Answer 1

To find the measure of angle HFG, we need to find the value of x first. We can do this by using the angles in the triangle and applying the angle sum property of a triangle. Once we have the value of x, we can substitute it into the equation for angle HFG to find its measure.

Step-by-step explanation:

To find the measure of angle HFG, we need to find the value of x first. We can do this by using the angles in the triangle. According to the angle sum property of a triangle, the sum of the angles in a triangle is always 180°.

So, we can set up the equation: (x-2)+(4x-5)+(x+19)=180

Simplifying this equation, we get: 6x+12=180. Solving for x gives us x=28.

Now that we have the value of x, we can substitute it into the equation for angle HFG: (x+19)° = (28+19)° = 47°

Therefore, the measure of ∠HFG is 47°, which corresponds to option B).