Mathematics

# In figure, line $l || m$ and $n$ is a transversal. If $\angle 1=40^o$, find all the angles and check that all corresponding angles and alternate angles are equal.

##### SOLUTION
As per the diagram $l||m$ and $n$ is transversal,
$\angle 1 = 40^o$

We know sum of angles on a straight line is $180^o$

$\angle 2 + 40 = 180^o$

$\angle 4 + 40 = 180^o$

=> $\angle 2 = 140^o$

=>  $\angle 4 = 140^o$

We know that Vertically opposite angles are equal

$\angle 1 = \angle 3 = 40^o$

$\angle 5 = \angle 7$

$\angle 6 = \angle 8$

We know that alternate interior angle are equal

$\angle 3 = \angle 5 = 40^o$     [ From  $\angle 3 = 40^o$]

$\angle 4 = \angle 6 = 140^o$      [ From  $\angle 4 = 140^o$]

Thus

$\angle 5 = \angle 7 = 40^o$        [ From  $\angle 5 = 40^o$]

$\angle 6 = \angle 8 = 140^o$       [ From  $\angle 6 = 140^o$]

$\therefore$ pair of corresponding angles are equal and alternate angles are equal

Corresponding angles

$\angle 1 =\angle 5 = 40^o$

$\angle 2 =\angle 6 = 140^o$

$\angle 3 =\angle 7 = 40^o$

$\angle 4 =\angle 8 = 140^o$

Alternate angles

$\angle 1 = \angle 7 = 40^o$

$\angle 2 = \angle 8 = 140^o$

$\angle 3 = \angle 5 = 40^o$

$\angle 4 = \angle 6 = 140^o$

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