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If line AC bisects angle BCD, what is the measure in d

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If line AC bisects angle BCD, what is the measure in d  [#permalink]

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New post 03 Mar 2019, 13:55
1
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (02:01) correct 29% (02:10) wrong based on 7 sessions

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GMATH practice exercise (Quant Class 1)

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If line AC bisects angle BCD, what is the measure of angle ADC?

(A) 20 degrees
(B) 30 degrees
(C) 40 degrees
(D) 45 degrees
(E) 50 degrees

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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Re: If line AC bisects angle BCD, what is the measure in d  [#permalink]

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New post 03 Mar 2019, 14:49
1
Lots of good lines/angles and triangles rules to refresh for this one:

-When two parallel lines are cut by a transversal, corresponding angles are equal
-Vertical angles are equal
-Supplemental angles sum to 180 degrees
-All the angles around one point sum to 360 degrees
-All three angles in a Triangle sum to 180 degrees

If you know all those rules and are comfortable with "extending lines," then this question isn't too challenging. :blushing
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If line AC bisects angle BCD, what is the measure in d  [#permalink]

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New post 03 Mar 2019, 15:00
fskilnik wrote:
GMATH practice exercise (Quant Class 1)

Image

If line AC bisects angle BCD, what is the measure of angle ADC?

(A) 20 degrees
(B) 30 degrees
(C) 40 degrees
(D) 45 degrees
(E) 50 degrees


Image

All angles are measured in degrees.

\(? = x\)

\(\Delta BCE\,\,:\,\,\,20 + x = 180 - \left( {110 + 20} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 30\)


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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If line AC bisects angle BCD, what is the measure in d   [#permalink] 03 Mar 2019, 15:00
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