Question

In the following figure, the side BC of ∆ ABC is extended up to the point D. If ∠A = 55° and ∠B = 60°, then the measure of ∠ACD is *
1 point
Captionless Image
(a) 120°
(b) 110°
(c) 115°
(d) 125°​

Answer 1

In the following figure, the side BC of ∆ ABC is extended up to the point D. If ∠A = 55° and ∠B = 60°, then the measure of ∠ACD is *

1 point

Captionless Image

(a) 120°

(b) 110°

(c) 115°

answer is c 115⁰

Answer 2

Given :   side BC of ∆ ABC is extended up to the point D

∠ A = 55° and ∠ B = 60°

To Find :  the measure of ∠ACD is

Solution:

Sum of angles of a triangle is 180°

=> ∠ A  + ∠ B   + ∠ C  = 180°

Substitute ∠ A = 55° and ∠ B = 60°

=> 55° + 60° + ∠ C  = 180°

=> ∠ C + 115°  = 180°

∠ C  is ∠ACB

=>   ∠ACB  + 115°  = 180°

Now ∠ACB  and ∠ACD form a linear pair as BC is extended to D

=> ∠ACB + ∠ACD = 180°

Equate both Equations:

∠ACB + ∠ACD =  ∠ACB  + 115°

=> ∠ACD =   115°

Hence  the measure of ∠ACD is 115°

Correct option is (c) 115°

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