Question

In figure, AB$||$CD and AC$||$BD. Find the values of $x,y,z$.

Answer 1

In figure, AB$||$CD and AC$||$BD and $\angle A={65}^0$

$\therefore \angle A$ and $\angle B$, $\angle A$ and $\angle C$, $\angle B$ and $\angle D$are pairs of supplementary angles.

And we know that, sum of supplementary angles is ${180}^0$

$\therefore \angle A+\angle B={180}^0$

$\therefore {65}^0+x={180}^0$

$\therefore x={115}^0$

Similarly,

$\angle A+\angle C={180}^0$

$\therefore {65}^0+z={180}^0$

$\therefore z={115}^0$

And

$\therefore \angle B+\angle D={180}^0$

$\therefore x+y={180}^0$

$\therefore {115}^0+y={180}^0$

$\therefore y={65}^0$