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555-605 (Medium)|   Geometry|      
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In the figure above, if AD is parallel to BC, then ∠ADC = 23 Jul 2020, 05:28
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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71% (02:09) correct 29% (02:35) wrong based on 170 sessions

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

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

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C
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In the figure above, if AD is parallel to BC, then ∠ADC = 23 Jul 2020, 05:42
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In Triangle BEC, \(\angle BCE\) = 180 - x - 44 = 136 - x (Sum of angles of a triangle = \(180^o\))

Since AD is parallel BC, \(\angle ADC\) + \(\angle BCD\) = \(180^o\) (Sum of interior angles between 2 parallel lines cut by a transversal = \(180^o\))

3x + 2x + 136 - x = 180

4x = 44

x = 11

\(\angle ADC\) = 3x = 3*11 = \(33^o\)

Option C

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In the figure above, if AD is parallel to BC, then ∠ADC = 23 Jul 2020, 05:47
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Bunuel

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

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

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Angle ADC = 3x = ?

Angle BCE = 180 - (X+44) = 136-x

Also, Angle BCD + Angle CDA = 180o (Parallel lines)

i.e. (136-x)+2x+3x = 180

i.e. 4x = 44
i.e. x = 11

hence, Angle ADC = 3x = 3*11 = 33o



Answer: Option C
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In the figure above, if AD is parallel to BC, then ∠ADC = 23 Jul 2020, 08:22
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We have, 180 - x - 44 + 2x + 3x = 180
=> 4x - 44 = 0
=> x = 11
ADC = 3x = 33

Hence, OA is (C).
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In the figure above, if AD is parallel to BC, then ∠ADC = 23 Jul 2020, 13:26
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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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In the figure above, if AD is parallel to BC, then ∠ADC = 26 Jul 2020, 17:06
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Bunuel

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

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

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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.

Answer: C
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In the figure above, if AD is parallel to BC, then ∠ADC = 28 Nov 2021, 07:47
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Bunuel

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

A. 11°

B. 22°

C. 33°

D. 46°

E. 134°

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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
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In the figure above, if AD is parallel to BC, then ∠ADC = 05 Feb 2023, 20:55
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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 = 06 Feb 2023, 02:21
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In the figure above, if AD is parallel to BC, then \(∠ADC = \)

3x + 2x + (180 - x - 44) = 180
4x = 44
\(∠ADC = 3x = 33 \)

IMO C
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