Question

"Question 3 In the given figure, if AB || DE, ∠BAC = 35º and ∠CDE = 53º, find ∠DCE.

Class 9 - Math - Lines and Angles Page 107"

Answer 1

angle DCE is 92°. is it helpful????????

Answer 2

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

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Solution:

Given:

AB||DE, ∠BAC=35∘ &

∠CDE=53∘

∠DEC=∠BAC=35∘ ….(i)    (alternate interior angles)

∠CDE=53∘       ……..(ii)       (given)

 

In, ∆CDE 

∠CDE+∠DEC+∠DCE=180°  

 

[sum of interior angles of a triangle is 180∘.]

 

⇒53∘+35∘+∠DCE=180∘ 

⇒88∘+∠DCE=180∘

 ⇒∠DCE=180∘−88∘=92∘

∠DCE=92°

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