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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If line AC bisects angle BCD, what is the measure in d

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

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Difficulty:   55% (hard)

Question Stats: 45% (02:01) correct 55% (03:12) wrong based on 11 sessions

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GMATH practice exercise (Quant Class 1) 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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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. Attachments IMG_2684.jpg [ 1.26 MiB | Viewed 413 times ]

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Reading Comprehension is my jam! GMATH Teacher P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 936
If line AC bisects angle BCD, what is the measure in d  [#permalink]

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fskilnik wrote:
GMATH practice exercise (Quant Class 1) 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 All angles are measured in degrees.

$$? = x$$

$$\left( 1 \right)\,\,{\text{angle}}\,\,DCE\,\,\, = \,\,\,20 + x\,\,\,\,\,\,\left[ {\,{\text{exterior}}\,\,{\text{angle}}\,\,{\text{of}}\,\,\Delta ADC\,} \right]$$

$$\left( 2 \right)\,\,{\text{angle}}\,\,ECB\,\,\, = \,\,\,20 + x\,\,\,\,\,\,\left[ {\,{\text{line}}\,\,AC\,\,{\text{bisects}}\,\,\,{\text{angle}}\,\,BCD\,} \right]$$

$$\left( 3 \right)\,\,{\text{angle}}\,\,DAC\,\,\, = \,\,\,{\text{angle}}\,\,AEB\,\,\, = \,\,\,20\,\,\,\,\,\,\left[ {\,{\text{lines}}\,\,AD\,\,{\text{and}}\,\,BE\,\,{\text{are}}\,\,{\text{parallel}}\,} \right]$$

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

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

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net If line AC bisects angle BCD, what is the measure in d   [#permalink] 03 Mar 2019, 14:00
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