The convex pentagon ABCDE has 4 sides: AB = BC = DE = AE. The angles at the vertices A and B

| February 16, 2021 | education

The convex pentagon ABCDE has 4 sides: AB = BC = DE = AE. The angles at the vertices A and B are straight, and at the vertex E it is 120 degrees. Find the angle at the vertex C.

Let’s draw an additional segment between the angles E and C. Because the sides AE, AB, BC are equal, and the angles A and B are straight, the segment EC will complete the square ABCE.
In a square, all corners will also be right.
The angle AEC is straight, so, knowing the angle AED, we find the angle CED:
120 ° – 90 ° = 30 °.
The sides of the square ABEC are equal and they are equal to the side ED of the triangle ECD.
Since the sides ED and EC of the triangle ECD are also equal, it is isosceles.
DC for it is the base, and the angles at the base of an isosceles triangle are equal.
Let’s find the sum of these angles:
180 ° – 30 ° = 150 °.
If their sum is equal to 150 °, then each of them is equal to half of the sum:
150 °: 2 = 75 °.
ANSWER: Angle C is 75 °.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.