Question

in the adjoining figure, if AB parallel to DE then find the measure of angle DCE​

Answer 1

Answer:

ab is parallel to de

Angle ced=angle bae(alternate angles)

angle ced=35

angle(EDC+CED+ECD)=180

53+35+DCE=180

ECD=92

Answer 2

Calculation of angle of a triangle.

Answer:

Measure of angle DCE that is m(∠DCE) = 92°.

Explanation:

Given that AB is parallel to DE .

first we will be using theorem which says that " Alternate interior angles are equal formed by a trasversal intersecting two parallel lines ".

From Figure AE can be treated as transversal cutting two parallel lines AB and DE.

so using above theorem we can say that

∠BAC = ∠CED     [ alternate interior angles ]

=> 35° = ∠CED  

=> ∠CED   = 35°

Now consider ΔCDE

Here we will be using angle sum property of triangle which says that sum of three angles of triangle is 180°.

=> ∠CED + ∠EDC + ∠DCE = 180°

=> 35° +  53° + ∠DCE = 180°

=>  ∠DCE = 180° - 88° = 92°

Hence measure of angle DCE that is m(∠DCE) = 92°.

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