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.
Hi swerve,
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.
