caculate angles of triangle abc having 3 times angle b= 4 times angle c and interior angle a =4/7  of its exterior angle

Asked by dvmathur | 14th Oct, 2019, 11:14: PM

Expert Answer:

Question:
 
Caculate angles of triangle abc having 3 times angle b= 4 times angle c and interior angle a =3/7  of its exterior angle
 
Solution:
 
Let ABC be the given triangle.
 
begin mathsize 16px style angle straight A space plus space angle straight B space plus space angle straight C space equals space 180 degree space.... left parenthesis 1 right parenthesis
3 angle straight B space equals space 4 angle straight C rightwards double arrow fraction numerator angle straight B over denominator angle straight C end fraction equals space 4 over 3
angle straight A space equals space 3 over 7 open parentheses Exterior space angle straight A space close parentheses space equals space 3 over 7 open parentheses space angle straight B space plus space angle straight C close parentheses
Let space angle straight B space equals space 4 straight x comma space angle straight C space equals space 3 straight x rightwards double arrow angle straight A space equals space 3 over 7 open parentheses space 4 straight x space plus space 3 straight x close parentheses space equals space 3 straight x
From space left parenthesis 1 right parenthesis comma space we space get
3 straight x space plus space 4 straight x space plus space 3 straight x space equals space 180 degree
rightwards double arrow straight x space equals space 18 degree
rightwards double arrow angle straight A space space equals space 54 degree space comma space angle straight B space equals space 72 degree space and space angle straight C equals space 54 degree




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Answered by Yasmeen Khan | 17th Oct, 2019, 11:44: AM