Question

∠ACH = 115°
∠GBF = 35°
What is the degree measure of ∠A?

Answer 1

A straight line is 180°. So you can do:

∠ACH + ∠ACB = 180° (you can do∠ACG or ∠ACB, doesn't matter)

This is because ∠ACH and ∠ACB make up a 180° angle(straight line)

∠ACH + ∠ACB = 180° Since you know ∠ACH, you can plug it in

115° + ∠ACB = 180° Subtract 115 on both sides to find ∠ACB

∠ACB = 65°

The ∠GBF should be equal to ∠ABC, so ∠ABC = 35°

This is because opposite angles are congruent/identical (equal)

A triangle is also 180°.

Now that you know the angle of C and B, you can do this:

65° + 35° + ∠A = 180°

100° + ∠A = 180° Subtract 100 on both sides

∠A = 80°

Answer 2

∠ACB is a Supplementary angle to ∠ACH. Supplementary angles must equal 180 degrees.

∠ACB = 180 - 115 = 65 degrees.

∠ABC is a vertical angle of ∠GBF, which means they are identical, so ∠ABC is 35 degrees.

The three inside angles of a triangle must equal 180 degrees.

∠A = 180 - 65 - 35 = 80 degrees