In a triangle ABC, if  angle A + angle B = 65

and  angle B +  angle C = 140

, then the measure of  angle B is

(a) 40

(b) 25

c) 115

(d) 60

Asked by swatipuspapatel | 7th Feb, 2021, 07:29: PM

Expert Answer:

Sum of all the angles of a triangle is 180°.
In ΔABC, 
 
begin mathsize 16px style straight m angle straight A space plus space straight m angle straight B space plus space straight m angle straight C space equals space 180 degree
rightwards double arrow 65 degree space plus space straight m angle straight C space equals space 180 degree space............ left parenthesis given space that space straight m angle straight A space plus space straight m angle straight B space equals space 65 degree right parenthesis
rightwards double arrow space straight m angle straight C equals 180 degree minus space 65 degree space equals space 115 degree space.... left parenthesis 1 right parenthesis

straight m angle straight B space plus space straight m angle straight C space equals space 140 degree space..... given
rightwards double arrow straight m angle straight B space plus 115 degree space equals space 140 degree
rightwards double arrow straight m angle straight B space space equals space 140 degree space minus 115 degree equals space 25 degree

end style

Answered by Yasmeen Khan | 8th Feb, 2021, 07:47: PM