227,851 views
21 votes
21 votes
Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel.

Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel-example-1
User Amirreza Noori
by
2.8k points

1 Answer

15 votes
15 votes

To begin we shall sketch a diagram of the line segments as given in the question

As depicted in the diagram, line segment AC is parallel to line segment DB.

This means angle A and angle B are alternate angles. Hence, angle B equals 41 degrees. Similarly, angle C and angle D are alternate angles, which means angle C equals 56.

Therefore, in triangle EAC,


\begin{gathered} \angle A+\angle C+\angle AEC=180\text{ (angles in a triangle sum up to 180)} \\ 41+56+\angle AEC=180 \\ \angle AEC=180-41-56 \\ \angle AEC=83 \end{gathered}

The measure of angle AEC is 83 degrees

Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel-example-1
User Rahul Vyas
by
2.5k points