Question

В треугольнике abc угол b равен 80 градусов на стороне BC отмечена точка D такая что AB=AD=CD на отрезке AC отмечена точка E такая что АВ=АЕ найлите угол СЕВ ПОМОГИТЕ ПЖ ПЖ ПЖ ПЖ СРОЧНО

Answer 1

Ответ:

110

Объяснение:угол равностронник по 1му признаку равенства

Answer 2

Finding the Angle SEV in Triangle ABC

To find the angle SEV in triangle ABC, we need to analyze the given information and apply relevant geometric principles.

Given: - In triangle ABC, angle B is 80 degrees. - Point D is marked on side BC such that AB = AD = CD. - Point E is marked on side AC such that AB = AE.

To find angle SEV, we can break down the problem into smaller steps:

Step 1: Find the value of angle A.

Since AB = AD, we can conclude that triangle ABD is an isosceles triangle. In an isosceles triangle, the base angles are equal. Therefore, angle ABD = angle ADB.

Similarly, since AB = AE, we can conclude that triangle ABE is also an isosceles triangle. Therefore, angle ABE = angle AEB.

Since the sum of the angles in a triangle is 180 degrees, we can write the following equation:

angle A + angle ABD + angle ABE = 180 degrees

Substituting the equal angles, we get:

angle A + angle ADB + angle AEB = 180 degrees

Since angle ADB and angle AEB are equal, we can rewrite the equation as:

angle A + 2 * angle ADB = 180 degrees

Simplifying the equation, we find:

angle A = 180 degrees - 2 * angle ADB

Step 2: Find the value of angle ADB.

Since AB = AD = CD, we can conclude that triangle ACD is an equilateral triangle. In an equilateral triangle, all angles are equal to 60 degrees.

Therefore, angle ADB = 180 degrees - angle ACD = 180 degrees - 60 degrees = 120 degrees.

Step 3: Find the value of angle A.

Substituting the value of angle ADB into the equation from Step 1, we get:

angle A = 180 degrees - 2 * 120 degrees = -60 degrees.

However, angles cannot be negative, so we need to adjust the value of angle A.

Since angle A is an interior angle of triangle ABC, it must be positive. Therefore, we can add 180 degrees to the negative value of angle A to obtain the positive value:

angle A = -60 degrees + 180 degrees = 120 degrees.

Step 4: Find the value of angle SEV.

To find angle SEV, we need to consider triangle AED. Since AB = AE, we can conclude that triangle AED is an isosceles triangle. Therefore, angle AED = angle ADE.

Since the sum of the angles in a triangle is 180 degrees, we can write the following equation:

angle AED + angle ADE + angle EDA = 180 degrees

Substituting the equal angles, we get:

angle AED + angle AED + angle EDA = 180 degrees

Simplifying the equation, we find:

2 * angle AED + angle EDA = 180 degrees

Since angle AED and angle EDA are equal, we can rewrite the equation as:

2 * angle AED + angle AED = 180 degrees

Simplifying further, we find:

3 * angle AED = 180 degrees

Dividing both sides of the equation by 3, we get:

angle AED = 180 degrees / 3 = 60 degrees.

Therefore, angle SEV = angle AED = 60 degrees.

Answer:

The angle SEV in triangle ABC is 60 degrees.