Answer:
- 78.33°
- 71°
Step-by-step 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°
