what are the measures of the unknown angles?

Question

the measure of one of the angles of a triangle is 35. the sum of the measures of the other two angles is 145 and the difference between their measures is 15.

Answer 1

let a,b,c are the angles of triangle.

Given c = 35

Now find a,b values

The sum of two angles is a+b =145 ---------> (1)

difference of two angles is a-b = 15 -----------> (2)

Add the equations (1) and (2)

a+b = 145

a-b = 15

_________

2a = 160

Divide to each side by 2.

2a/2 = 160/2

a = 80

Substitute the a value in (1).

80+b = 145

Subtract 80 from each side.

80-80+b = 145-80

b = 65

So the angles of triangle is 35,65,80.