11. find each measure. m< 1, m< 2, m< 3

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

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step-by-step explanation:

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