In the figure above, if \(AD\) is parallel to \(BC,\) then \(\angle ADC=\angle ADC=\)
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A
B
C
D
E
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A. \(11^{\circ}\)
B. \(22^{\circ}\)
C. \(33^{\circ}\)
D. \(46^{\circ}\)
E. \(134^{\circ}\)
Answer: C
Source: Princeton Review
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First, since angles in a triangle must add to 180°, we can see that the missing angle in the red triangle must be 180° - (x + 44)°
Simplify this measurement to get (136 - x)°
Finally, since AD is parallel to BC, we know that the two highlighted angles below must add to 180°.
So, we can write: (136 - x)° + 2x° + 3x° = 180°
Simplify: 136 + 4x = 180
Subtract 136 from both sides: : 4x = 44
Solve: x = 11
Our goal is to find the measurement of ∠ADC
Since ∠ADC = 3x°, we can replace x with 11 to get: ∠ADC = 3x° = 3(11)° = 33°
Answer: C