Question

In figure,lines AB and CD intersect each other at point O.If a:b = 4:5, find a,b,c and d.

Answer 1

In figure, ray OA, stands on the line CD.

Therefore a + b= 180${}^{\circ }$ (Linear pair of angles)

It is given that a : b = 4 : 5

There, we have sum of the ratios =4 + 5=9

a= 180${}^{\circ }$ $\times$ $\frac{4}{9}$ = 80${}^{\circ }$, and b = 180${}^{\circ }$ $\times$$\frac{5}{9}$ = 100${}^{\circ }$

Now ,c = a = 80${}^{\circ }$ and d = b = 100${}^{\circ }$ (vertically opposite angles)

Hence, a = 80${}^{\circ }$ , b = 100${}^{\circ }$ , c = 80${}^{\circ }$ and d = 100${}^{\circ }$