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In the figure above, if AD is parallel to BC, then ∠ADC = : Problem Solving (PS)
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# In the figure above, if AD is parallel to BC, then ∠ADC =

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We have, 180 - x - 44 + 2x + 3x = 180
=> 4x - 44 = 0
=> x = 11

Hence, OA is (C).
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From the problem drawing, we can tell Angle ADC must be a multiple of 3

Taking a quick look at the answer choices, there's only one answer which fits

Thus, x must be 11 and angle ADC equals 33

IMO C
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Bunuel wrote:

In the figure above, if AD is parallel to BC, then $$∠ADC =$$

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

Attachment:
1.jpg

Solution:

Letting angle BCE = y, we have:

(y + 2x) + 3x = 180 (since consecutive angles of a parallelogram add up to 180 degrees)

and

y + x + 44 = 180 (since the sum of the measures of the 3 angles of a triangle is 180 degrees)

Since the right hand sides of both equations above is 180, we can set the left hand sides equal to each other.

(y + 2x) + 3x = y + x + 44

5x = x + 44

4x = 44

x = 11

Since angle ADC = 3x, angle ADC = 3(11) = 33 degrees.

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Bunuel wrote:

In the figure above, if AD is parallel to BC, then $$∠ADC =$$

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

Attachment:
1.jpg

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°

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Please find the solution for the question
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In the figure above, if AD is parallel to BC, then $$∠ADC =$$
$$∠ADC = 3x = 33$$