Question

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Answer 1

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FORMULA TO BE IMPLEMENTED

THEOREM : 1

If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.

THEOREM : 2

If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal.

PROBLEM : 1 ( Fig 6.135)

It is given that

AB || CD &

$\angle \: BAE = {110}^{ \circ \:} \: \: and \: \: \angle ECD \: = {120}^{ \circ}$

Construction

Draw a line GH parallel to AB & CD

Now by the Theorem 1

$\angle \: BAE + \angle \: AEH \: = {180}^{ \circ \:}$

$\implies \: \angle \: AEH \: = {180}^{ \circ \:} - {110}^{ \circ \:} = {70}^{ \circ \:}$

Again

$\angle ECD \: + \angle \: CEH = {180}^{ \circ}$

$\implies \: \angle \: CEH = {180}^{ \circ} - {120}^{ \circ} = {60}^{ \circ}$

Hence

$X = {70}^{ \circ} + {60}^{ \circ} = {130}^{ \circ}$

PROBLEM : 2 ( Fig 6.136)

It is given that AB || CD

$\angle \: ABE = {35}^{ \circ \:} \: \: and \: \: \angle CDE \: = {65}^{ \circ}$

Construction

Construction Draw a line GH parallel to AB & CD

By the Theorem 2

$\angle \: BEG \: = \: \angle \: ABE = {35}^{ \circ \:}$

And

$\angle \: DEG \: = \: \angle CDE \: = {65}^{ \circ}$

Hence

$X = {35}^{ \circ} + {65}^{ \circ} = {100}^{ \circ}$

Answer 2

Answer:

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