Question

Через вершину C трапеции ABCD проведена прямая , которая параллельна боковой стороне AB и и пересекает большее основание AD в точке E найдите углы трапеции если угол D=35 ,DCE=65

Answer 1

/CED=180-(65+35)=80
CEA=180-80=100 (т.к смежные )
ВСЕ=СED=80 т.к накрест лежащие
С=80+65=145
AB Паралельна CE зн. ABCE паралерограмм
CEA=CBA=100
BAE=BCE=80

Answer 2

Given Information

We have a trapezoid ABCD, with a straight line passing through the vertex C, parallel to the side AB. This line intersects the longer base AD at point E. We are given that angle D is 35 degrees and angle DCE is 65 degrees.

Approach to solve the problem

To find the angles of the trapezoid, we can use the properties of parallel lines and the angles formed by the transversal.

Solution

Let's label the angles in the trapezoid as follows: - Angle A = α - Angle B = β - Angle C = γ - Angle D = 35 degrees

Since the line passing through vertex C is parallel to side AB, we can conclude that angle C and angle B are alternate interior angles, and therefore they are congruent. So, angle C = β.

Since angles DCE and BCD are supplementary angles (they form a straight line), we can find angle BCD by subtracting angle DCE from 180 degrees. So, angle BCD = 180 - 65 = 115 degrees.

Now, we can use the fact that the sum of the angles in a trapezoid is equal to 360 degrees to find the remaining angle.

The sum of the angles in a trapezoid is given by: α + β + γ + 35 = 360

Substituting the values we know: α + β + β + 35 = 360

Simplifying the equation: α + 2β + 35 = 360

Subtracting 35 from both sides: α + 2β = 325

We have one equation with two variables, so we cannot solve for the individual values of α and β. However, we can find the relationship between them.

Since angle BCD is congruent to angle ACD (they are opposite angles), we can conclude that angle ACD is also 115 degrees.

So, angle A + angle C + angle D = 180 degrees: α + γ + 35 = 180

Substituting the value of γ as β: α + β + 35 = 180

Simplifying the equation: α + β = 145

Now, we have a system of equations: α + 2β = 325 α + β = 145

Subtracting the second equation from the first equation: α + 2β - (α + β) = 325 - 145 β = 180

Substituting the value of β back into the second equation: α + 180 = 145 α = 145 - 180 α = -35

Since we cannot have negative angles, we conclude that there is no solution for the given angles.

Therefore, the angles of the trapezoid cannot be determined with the given information.