Answer: Choice D
angle 1 = 75 degrees
angle 2 = 129 degrees
angle 3 = 100 degrees
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Explanation:
Refer to the diagram below. I have marked points A through F on the diagram, as well as add variables x and y (the green angles). We are given
Angle BAC = 54
Angle ACB = 46
Angle CBD = 29
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Focus on triangle CDB
Solve for x
(angle BDC)+(angle DCB)+(angle DBC) = 180
x+46+29 = 180
x+75 = 180
x = 180-75
x = 105
We can use this to find angle 1
angle 1 = 180-(angle BDC)
angle 1 = 180-x
angle 1 = 180-105
angle 1 = 75
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Move onto triangle ABC
Find angle ABC which is equal to y+29
(angle ABC) + (angle ACB) + (angle CAB) = 180
(y+29) + (46) + (54) = 180
y+129 = 180
y = 180-129
y = 51
angle ABC = y+29
angle ABC = 51+29
angle ABC = 80
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(angle CBG) + (angle ABC) = 180
(angle CBG) + 80 = 180
angle CBG = 180-80
angle CBG = 100
angle 3 = 100
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Finally,
angle 2 = (angle DBC)+(angle CBG)
angle 2 = 29+100
angle 2 = 129
