In the given figure, line m is parallel to n. Given that
`angle BAP=3x+10^(@),angleBAC=3x`
` angleABC=3y-5^(@),angleACB=x+y+5^(@)`
Find the valuses of x and y

Explanation

Given line m|| line x
`:. anglePAB=angleABC" ".` (alternate angles)
`rArr 3x+10^(@)=3y-5^(@)`
`rArr 3x-xy=-15^(@)`
Now, `angle (BAC+angleCBA+angleACB=180^(@)" "` (sum of all angles of a triangles is `180^(@))`
`rArr 3x+(3y-5^(@)) +(x+y+5^(@)) =180^(@)`
`rArr 4x+4y=180^(@)`
`rArr x+y=45^(@)`
Solving equations (1) and (2), we get
`x=20^(@) and =25^(@)`