of exterior ZA, 10. Calculate the angles of a triangle ABC having 34B = 4ZC and the interior ZA =

Asked by bhartinandanfans | 27th Aug, 2020, 11:12: AM

Expert Answer:

The question should be:
Calculate the angles of a triangle ABC having 3 angleB = 4 angleC and the interior angleA = 3/7 exterior angleA
Solution:
3 angle straight B equals 4 angle straight C space... space left parenthesis straight i right parenthesis
Interior angle straight A equals 3 over 7 Ext. angle straight A space... space left parenthesis ii right parenthesis
Now comma space ext. angle straight A equals angle straight B plus angle straight C space
rightwards double arrow space angle straight A equals 3 over 7 open parentheses angle straight B plus angle straight C close parentheses space.... space left parenthesis iii right parenthesis
We space know space that space angle straight A plus angle straight B plus angle straight C equals 180
rightwards double arrow angle straight B plus angle straight C equals 180 degree minus angle straight A space... space left parenthesis iv right parenthesis
Substituting space this space in space left parenthesis iii right parenthesis comma space we space get
angle straight A equals 3 over 7 open parentheses 180 degree minus angle straight A close parentheses
rightwards double arrow angle straight A equals 54 degree
Substituting space this space in space left parenthesis iv right parenthesis comma space we space get
angle straight B plus angle straight C equals 180 degree minus 54 degree equals 126 degree
rightwards double arrow angle straight B equals 126 degree minus angle straight C space... space left parenthesis straight v right parenthesis
From space left parenthesis straight i right parenthesis comma space we space get
3 open parentheses 126 degree minus angle straight C close parentheses equals 4 angle straight C
rightwards double arrow angle straight C equals 54 degree
Putting space this space in space left parenthesis straight v right parenthesis comma space we space get
angle straight B equals 72 degree

Answered by Renu Varma | 27th Aug, 2020, 11:48: AM