M7MBA wrote: ↑

Sun Nov 28, 2021 1:16 am

1.jpg

In the figure above, if \(AD\) is parallel to \(BC,\) then \(\angle ADC=\angle ADC=\)

A. \(11^{\circ}\)

B. \(22^{\circ}\)

C. \(33^{\circ}\)

D. \(46^{\circ}\)

E. \(134^{\circ}\)

Answer: C

Source: Princeton Review

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