Question

Answer the following.

Answer 1

1. 78.33°
2. 71°

Explanation:

1) The sum of angles in a triangle is 180°, so ...

(x +3)° +(x +24)° +(x -10)° = 180°

3x +17 = 180 . . . . . . . . divide by °, collect terms

3x = 163 . . . . . . . . . . . .subtract 17

x = 54 1/3 . . . . . . . . . . .divide by 3

m∠B = (x +24)° = (54 1/3 + 24)°

m∠B ≈ 78.33°

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2) An exterior angle is equal to the sum of the opposite interior angles.

m∠ACD = m∠A + m∠B

(3x -10)° = (x +9)° + 105°

2x = 124 . . . . . . . . . . . . . . divide by °, add 10-x to both sides

x = 62 . . . . . . . . . . . . . . . . divide by 2

m∠A = (x +9)° = (62 +9)°

m∠A = 71°