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

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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

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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