Question

In the figure, AB || CD and $\angle 1$ and $\angle 2$ are in the ratio 3:2. Determine all angles from 1 to 8.

Answer 1

AB || CD and l is transversal $\angle 1:\angle 2=3:2$
Let $\angle 1=3x$
Then $\angle 2=2x$
But $\angle 1+\angle 2={180}^0$ (Linear pair)
$\therefore 3x+2x={180}^0\Rightarrow 5x={180}^0$
$\Rightarrow x=\frac{{180}^0}{5}={36}^0$
$\therefore \angle 1=3x=3\times {36}^0={108}^0$
$\angle 2=2x=2\times {36}^0={72}^0$
Now $\angle 1=\angle 3and\angle 2=\angle 4$
(Vertically opposite angles)
$\therefore \angle 3={108}^{0}and\angle 4={72}^0$
$\angle 1=\angle 5and\angle 2=\angle 6$
(Corresponding angles)
$\therefore \angle 5={108}^0,\angle 6={72}^0$
Similarly, $\angle 4=\angle 8$ and
$\angle 3=\angle 7$
$\therefore \angle 8={72}^{0}and\angle 7={108}^0$
Hence, $\angle 1=\angle {108}^0,\angle 2=\angle {72}^0$
$\angle 3={108}^0,\angle 4={72}^0\angle 5={108}^0,\angle 6={72}^0\angle 7={108}^0,\angle 8={72}^0$