Question

in a triangle an exterior angle at a vertex is 95 degree and its one of the interior opposite angle is 55 degree find all the angle of the triangle

Answer 1

Hi ,

In a triangle an exterior angle at a vertex is

equal to sum of interior opposite angles.

Let three angles are A , B and C ,

according to the problem given,

exterior angle at C = 95

let <B = 55

exterior angle at C = <A + <B

95 = <A + 55

95 - 55 = <A

<A = 40


sum of the angles in a triangle = 180°

<A + <B+ <C = 180

40 + 55 + <C = 180

95 + <C = 180

<C = 180 - 95

<C = 85°

I hope this helps you.

:)

Answer 2

let ABC the triangle
where C is produced to D
angle ACD now ext angle=95degrees
one of opp. side is 55
A/Q,
ACD=CAB+ABC (EXT ANGLE FORMULA)
95=55+ABC
ABC=40DEGREE
NOW,
CAB+ACB+ABC=180 (ANGLE SUM PRO.)
95+ACB=180
ACB=85 degree