∠ ACD is an exterior angle of ∆ ABC , ∠B = 50° ,∠A = 80° . Find the measure of ∠ACD
Answers
Given : side BC of ∆ ABC is extended up to the point D so that ∠ACD is exterior angle
∠ A = 80° and ∠ B = 50°
To Find : the measure of ∠ACD is
Solution:
Sum of angles of a triangle is 180°
=> ∠ A + ∠ B + ∠ C = 180°
Substitute ∠ A = 80° and ∠ B = 50°
=> 80° + 50° + ∠ C = 180°
=> ∠ C + 130° = 180°
∠ C is ∠ACB
=> ∠ACB + 130° = 180°
Now ∠ACB and ∠ACD form a linear pair as BC is extended to D
=> ∠ACB + ∠ACD = 180°
Equate both Equations:
∠ACB + ∠ACD = ∠ACB + 130°
=> ∠ACD = 130°
Hence the measure of ∠ACD is 130°
Shortcut:
Exterior angle of Triangle = Sum of opposite two interior angles
Hence ∠ACD = 50° + 80° = 130°
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