BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The figure shows that line m is parallel to the line n, and

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

The figure shows that line m is parallel to the line n, and

by Max@Math Revolution » Sun Oct 13, 2019 11:13 pm
[GMAT math practice question]

The figure shows that line m is parallel to the line n, and l is parallel to k. Moreover, ∠ CBD=45, ∠ FAE=80. What is ∠ BDC?

Image

A. 40
B. 45
C. 50
D. 55
E. 60
Top
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Thu Jul 18, 2019 5:59 am

by Aditi Goyal » Mon Oct 14, 2019 12:44 am
Angle EAF is vertically opposite to angle BAD. Angle EAF=80
Therefore Angle BAD = 80
SInce m||n and l || k, it is a forms a parallelogram
Angle BAD = Angle BCD (opposite angles) = 80
In triangle BCD, angle BDC = 180 -(80+45) = 55
therefore angle BCD = 80 $$\angle$$ $$\angle$$
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Thu Jul 18, 2019 5:59 am

by Aditi Goyal » Mon Oct 14, 2019 12:47 am
Aditi Goyal wrote:Angle EAF is vertically opposite to angle BAD. Angle EAF=80
Therefore Angle BAD = 80
SInce m||n and l || k, it forms a parallelogram
Angle BAD = Angle BCD (opposite angles) = 80
In triangle BCD, angle BDC = 180 -(80+45) = 55
therefore angle BCD = 80 $$\angle$$ $$\angle$$
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Wed Oct 16, 2019 1:14 am
=>

Image

Since lines m and n are parallel, we have < FBG=< FAE=80° and 80°+< ABD+45°=180°.
Then we have 125°+< ABD=180 and < ABD=55°.
Since < ABD and < BDC are alternate interior angles, they are congruent and < BDC=55°.

Therefore, D is the answer.
Answer: D
Top
Post new topic Post Reply
• Page 1 of 1