In the given figure, the arms of two angles are parallel. If $\angle ABC = 70^{\circ}$, then find

$(i).\ \angle DGC$
$(ii).\ \angle DEF$"

Given:

In the given figure, the arms of two angles are parallel.

$\angle ABC = 70^{\circ}$.

To do:

We have to find

(i) $\angle DGC$

(ii) $\angle DEF$

Solution:

$AB \| DE$                 [Given]

$BC \| EF$                  [Given]

$\angle ABC=70^{\circ}$

$\angle ABC$ and $\angle DEF$ are a pair of corresponding angles.

This implies,

$\angle DEF=\angle ABC$

(i) $AB \| DE$

This implies,

$AB \| DG$

$\angle DGC=\angle ABC=70^{\circ}$                 [Pair of corresponding angles]

(ii) $BC \| EF$

This implies,

$GC \| EF$

$\angle DEF=\angle DGC=70^{\circ}$               [Pair of corresponding angles]

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Updated on: 10-Oct-2022

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