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03 Mar 2019, 13:55
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B
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Difficulty:
55%
(hard)
Question Stats:
59% (02:25) correct
41%
(02:39)
wrong
based on 68
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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
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
03 Mar 2019, 14:49
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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.
-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.
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03 Mar 2019, 15:00
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fskilnik
All angles are measured in degrees.
\(? = x\)
\(\left( 1 \right)\,\,{\text{angle}}\,\,DCE\,\,\, = \,\,\,20 + x\,\,\,\,\,\,\left[ {\,{\text{exterior}}\,\,{\text{angle}}\,\,{\text{of}}\,\,\Delta ADC\,} \right]\)
\(\left( 2 \right)\,\,{\text{angle}}\,\,ECB\,\,\, = \,\,\,20 + x\,\,\,\,\,\,\left[ {\,{\text{line}}\,\,AC\,\,{\text{bisects}}\,\,\,{\text{angle}}\,\,BCD\,} \right]\)
\(\left( 3 \right)\,\,{\text{angle}}\,\,DAC\,\,\, = \,\,\,{\text{angle}}\,\,AEB\,\,\, = \,\,\,20\,\,\,\,\,\,\left[ {\,{\text{lines}}\,\,AD\,\,{\text{and}}\,\,BE\,\,{\text{are}}\,\,{\text{parallel}}\,} \right]\)
\(\Delta BCE\,\,:\,\,\,20 + x = 180 - \left( {110 + 20} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 30\)
The correct answer is (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
