Question

The sum of two angles of a triangle is 116° and their difference is 24°.Find the measure of each angle of triangle​

Answer 1

Step-by-step explanation:

let x and y be the two angles

given x+y= 116 and x-y =24

add them we get 2x= 140 and x=70

substitute x in above eq

x+y=116

70+y=116 i.e.y=46

in triangle sum of three angles is 180

let the third angle is z

x+y+z=180

70+46+z=180

116+z=180

z=64. the angles of triangle are 70,46 and 64

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Answer 2

Let the first angle be x and the 2nd one be y.

acc. to given statement, x+y = 116° - - ( eq. 1)

and x-y = 24 - - ( eq. 2)

equating equation 1 and 2,

we get, x = 70°

we know, x+y = 116

so, 70+y = 116

y = 46°

so, adding all the angles of the triangle,

70+46+3rd angle = 180°

116+3rd angle = 180

so, 3rd angle = 64°

All the angles of the triangle are 64°,70° and 46°.

Hope it helps u!!