Question

The interior angles of a triangle are

(

5

x

+

3

y

)

∘

,

(

3

x

+

20

)

∘

,

and

(

10

y

+

30

)

∘

(5x+3y)∘,(3x+20)∘, and (10y+30)∘

, where

x

x

and

y

y

are positive integers. What is the value of

x

+

y

x+y

?

Answer 1

`8x+13y = 130`

Explanation:

sum of interior angles in a triangle is 180 degree

interior angles are (5x+3y)∘,(3x+20)∘, and (10y+30)

add all the angles and make it equal to 180

`5x+3y+3x+20+10y+30= 180`

combine like terms

`5x+3y+3x+20+10y+30= 180`

`8x+13y+x+50= 180`

subtract 50 from both sides

`8x+13y = 130`