find the measure of the smallest angle , angle hfg , if angle ghf=92 degrees and angle hgf = 72 degrees

the answer is 16

answered here by Steve

http://www.jiskha.com/display.cgi?id=1352220822

To find the measure of angle HFG, we can use the fact that the sum of angles in a triangle is 180 degrees.

Let's assume that angle HFG measures x degrees.

Given:
Angle GHF = 92 degrees
Angle HGF = 72 degrees

According to the sum of angles in a triangle:
Angle GHF + Angle HGF + Angle HFG = 180

Substituting the given values:
92 + 72 + x = 180

Simplifying the equation:
164 + x = 180

Subtracting 164 from both sides of the equation:
x = 180 - 164

x = 16

Therefore, the measure of angle HFG, or angle "hfg," is 16 degrees.

To find the measure of the smallest angle, angle HFG, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

In this case, the three angles of the triangle are angle GHF, angle HGF, and angle HFG. We know that angle GHF is 92 degrees and angle HGF is 72 degrees.

Step 1: Start with the sum of the measures of the three angles in the triangle:
angle GHF + angle HGF + angle HFG = 180 degrees

Step 2: Substitute the values we know:
92 + 72 + angle HFG = 180 degrees

Step 3: Simplify the equation:
164 + angle HFG = 180 degrees

Step 4: Solve for angle HFG:
angle HFG = 180 degrees - 164 degrees = 16 degrees

Therefore, the measure of the smallest angle, angle HFG, is 16 degrees.