What is the measure of angle E?
This topic has expert replies
https://postimg.cc/image/dz0biwzd9/ (zoom here)
In the diagram above, angles measures in degrees are marked as shown, and segment BC is parallel to line AD. What is the measure of angle E?
(A) 30°
(B) 35°
(C) 40°
(D) 45°
(E) 50°
The OA is D.
Please, can any expert explain this PS question for me? I tried to solve it but I don't understand it. I need your help. Thanks.
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi swerve,In the diagram above, angles measures in degrees are marked as shown, and segment BC is parallel to line AD. What is the measure of angle E?
(A) 30°
(B) 35°
(C) 40°
(D) 45°
(E) 50°
The OA is D.
Please, can any expert explain this PS question for me? I tried to solve it but I don't understand it. I need your help. Thanks.
Let's take a look at your question.
In triangle ABC,
$$\angle BCA=180-\angle BAC-\angle ABC$$
$$\angle BCA=180-75-65$$
$$\angle BCA=40$$
Since, segment BC is parallel to the line AD, therefore, alternate interior angles are congruent.
$$\angle CAD=\angle BCA$$
$$\angle CAD=40$$
Consider triangle ADE,
$$\angle E=180-\angle D-\angle DAE$$
$$\angle E=180-95-40$$
$$\angle E=45$$
Therefore, Option D is correct.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.