Question

Point D is the incenter of triangle BCA. If m∠FDG=136°, what is the measure of ∠FHG?

A) 68°
B) 44°
C) 136°
D) 88°

Answer 1

To find the measure of angle FHG, we need to understand the properties of an incenter of a triangle. The incenter is the point of concurrency of the triangle's angle bisectors. Using this property, we can calculate the measure of angle FHG.

Step-by-step explanation:

To find the measure of angle FHG, we need to understand the properties of an incenter of a triangle.

The incenter of a triangle is the point of concurrency of the angle bisectors of the triangle. This means that FD, DG, and FG are all angle bisectors of triangle BCA.

Since FD bisects angle BCA, we can find the measure of angle BFA by using the property that the sum of the angles in a triangle is 180 degrees. Therefore, angle BFA = (180 - 136) / 2 = 72 degrees.

Similarly, angle DGA = (180 - 136) / 2 = 72 degrees.

Finally, since angle BFA and angle DGA are adjacent angles that form a straight line, we can find the measure of angle FHG by subtracting the sum of angle BFA and angle DGA from 180 degrees. Therefore, angle FHG = 180 - (72 + 72) = 36 degrees.

So, the measure of angle FHG is 36 degrees.