## 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

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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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