VJesus12 wrote: ↑

Sat Jan 01, 2022 1:15 pm

4.jpg

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

\(A.\, 11^\circ\)
\(B.\, 22^\circ\)
\(C.\, 33^\circ\)
\(D.\, 46^\circ\)
\(E.\, 134^\circ\)

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