9514 1404 393
Answer:
- x = 40
- x = 64
- x = 12
Step-by-step explanation:
Assuming the lines that look parallel are parallel, all of the acute angles are congruent, and all of the obtuse angles are congruent. Any obtuse angle is the supplement of any acute angle.
1)
∠C = ∠F
3x -10 = x +70 . . . . substitute the given values
2x = 80 . . . . . . . . . add 10-x
x = 40
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2)
∠D +∠F = 180
(x +27) +(2x -39) = 180 . . . . substitute
3x -12 = 180 . . . . . . . . . . . . . simplify
x -4 = 60 . . . . . . . . . . . divide by 3
x = 64 . . . . . . . . . add 4
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3)
∠B = ∠G
2(x +40) = 5x +44 . . . . . substitute
2x +80 = 5x +44 . . . . . . simplify
36 = 3x . . . . . . . . subtract 2x+44
12 = x . . . . . . divide by 3
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Additional comment
If you use the given values of x to find the angle measures, you quickly see that the figure is not drawn to scale, and that angles shown as acute may actually be obtuse.
