चित्र में, दिए गया है की ` AB||CD`
यदि ` angle 2= (2x+30) ^(@) ,angle 4=(x+2y)^(@) ` तथा ` angle 6=(3y+10)^(@) `, तो `angle 5` को मान ज्ञात कीजिए|

Explanation

दिया है
` " "angle 2=angle 4 " "` [शीर्षाभिमुख कोण ]
तथा ` " "angle 4=angle 6 " " ` [एकांतर कोण ]
` therefore " "angle 2=angle4=angle 6 `
परन्तु ` " "angle 2=angle 4 `
` rArr" "2x + 30 =x+ 2y`
`rArr " "2x-x-2y +30 =0`
`rArr " "x- 2y +30 =0`
तथा ` " "angle4=angle 6 " "...(i)`
`rArr" "(x+ 2y) =(3y+10) `
` rArr " " x-y-10 =0 " "...(iii)`
समीकरण (i ) में से (ii ) घटाने पर,
` " " (x-2y+30) -(x-y-10) =0rArr-y +40 =0rArry=40`
समीकरण (ii ) में y =40 मान रखने पर x =50
` therefore " "angle 4= (x+ 2y )^(@) =(50+2xx40)^(@) =130^(@)`
परन्तु ` " "angle 4+ angle 5 =180^(@) `
` therefore " " 130^(@) +angle 5=180^ (@) rArr angle 5=50^(@) `