Calculate the angles of a triangle ABC having 3 B = 4C and the interior A =3/7
of exterior A.
Answers
Calculation of Angles of triangle
Answer: ∠ A = 54° , ∠B = 72° and ∠C = 54° ( A , B and C are all interior angles of triangle ABC ) .
Explanation:
given that in triangle ABC
3B = 4C ,
And interior angle A = 3/7 of exterior Angle A.
lets assume exterior angle A = y degree
so interior angle A = (3/7) x y = 3y/7
interior angle of triangle and its exterior angle always forms a linear pair.
=> interior angle A + exterior Angle A = 180
=> (3y/7 ) + y = 180
=> 10y/7 = 180
=> y = (180 x 7) / 10 = 126
so interior angle A = 3y/7 = 3 x 126 / 7 = 54
As 3B = 4C
=> C = (3/4) B -------(1)
In triangle ABC
angle A + Angle B + angle C = 180 [ Angle sum property of triangle ]
=> 54 + B + (3/4)B = 180 [ Since C = (3/4) B and interior angle A = 54 ]
=> 7B/4 = 180 - 54 = 126
=> B = (126 x 4)/7 = 72
From (1) , C = (3/4) B = (3/4) x 72 = 54
Hence ∠ A = 54° , ∠B = 72° and ∠C = 54° ( A , B and C are all interior angles of traingle ABC ) .
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