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In the figure above if BC || AD, then x =
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29 Sep 2019, 08:08
29 Sep 2019, 08:08
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In the figure above if BC || AD, then x =
A. 20
B. 40
C. 45
D. 65
E. 115
Re: In the figure above if BC || AD, then x =
[#permalink]
29 Sep 2019, 22:30
29 Sep 2019, 22:30
Extend the shorter line segment out from A to C; this now makes line AC.
AC now touches two parallel lines (BC and AD), and we know there is a rule which states the opposite and diagonal angles of lines touching or crossing parallel lines are equal. This means that angle BCD is equal to angle CAD.
Since angle CAD is equal to 20 degrees, then angle BCD is equal to 20 degrees as well.
Finally, we know that a triangle is 180 degrees, hence triangle ABC's three angles add up to 180 degrees. We subtract for the value of degree x: 180 degrees - 20 degrees- 115 degrees = 45 degrees.
AC now touches two parallel lines (BC and AD), and we know there is a rule which states the opposite and diagonal angles of lines touching or crossing parallel lines are equal. This means that angle BCD is equal to angle CAD.
Since angle CAD is equal to 20 degrees, then angle BCD is equal to 20 degrees as well.
Finally, we know that a triangle is 180 degrees, hence triangle ABC's three angles add up to 180 degrees. We subtract for the value of degree x: 180 degrees - 20 degrees- 115 degrees = 45 degrees.
gmatclubot
Re: In the figure above if BC || AD, then x = [#permalink]
29 Sep 2019, 22:30
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