## In the diagram above, angle measures in degrees are marked as shown, and segment BC is parallel to line AD.

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### In the diagram above, angle measures in degrees are marked as shown, and segment BC is parallel to line AD.

by BTGmoderatorDC » Mon Aug 30, 2021 10:59 pm

00:00

A

B

C

D

E

## Global Stats In the diagram above, angle 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°

OA D

Source: Magoosh

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### Re: In the diagram above, angle measures in degrees are marked as shown, and segment BC is parallel to line AD.

by swerve » Tue Aug 31, 2021 2:49 am
BTGmoderatorDC wrote:
Mon Aug 30, 2021 10:59 pm
two triangles on a line.JPG

In the diagram above, angle 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°

OA D

Source: Magoosh
Try as follows:

Step 1: Since angles $$A$$ and $$B$$ are given, we can find the value of angle $$C,$$ it has to be $$40^{\circ},$$ because the sum of all interior angles in a triangle ($$ABC$$ in this case) must be $$180^{\circ}.$$

Step 2: Therefore, angle $$EAD$$ has to be also $$40^{\circ}$$ (i.e. equal to $$ACB$$), since we are given that $$AD \parallel BC.$$

Step 3: Finally, angle $$DEA$$ must be $$45^{\circ},$$ because (again) the sum of all interior angles in a triangle must be $$180^{\circ}.$$

Therefore, D

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