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

Given:

$AB \parallel CD$ and $\angle 1$ and $\angle 2$ are in the ratio $3 : 2$.

To do:

We have to find all angles from 1 to 8.

Solution:

We know that,

Vertically opposite angles are equal.

Corresponding angles are equal.

Therefore,

$AB \parallel CD$ and $l$ is transversal.

$\angle 1 : \angle 2 = 3 : 2$

Let $\angle 1 = 3x$

This implies,

$\angle 2 = 2x$

$\angle 1 + \angle 2 = 180^o$         (Linear pair)

$3x + 2x = 180^o$

$5x = 180^o$

$x = \frac{180^o}{5}$

$x = 36^o$

Therefore,

$\angle 1 = 3x = 3(36^o) = 108^o$

$\angle 2 = 2x = 2(36^o) = 72^o$

$\angle 1 = \angle 3$                       (Vertically opposite angles)

$\angle 2 = \angle 4$                       (Vertically opposite angles)

$\angle 3 = 108^o$

$\angle 4 = 72^o$

$\angle 1 = \angle 5$                       (Corresponding angles)

$\angle 2 = \angle 6$                       (Corresponding angles)

$\angle 5 = 108^o$

$\angle 6 = 72^o$

$\angle 4 = \angle 8$                       (Corresponding angles)

$\angle 3 = \angle 7$                       (Corresponding angles)

$\angle 8 = 72^o$

$\angle 7 = 108^o$

Hence, $\angle 1 = 108^o, \angle 2 = 72^o, \angle 3 = 108^o, \angle 4 = 72^o, \angle 5 = 108^o, \angle 6 = 72^o, \angle 7 = 108^o, \angle 8 = 72^o$.

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Updated on: 10-Oct-2022

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