Question

in the following figure a pair of parallel line are cut by a transversal . find the measure each lettered angle​

Answer 1

${\red{\underline{\underline{\bold{Given:-}}}}}$

• The pair of lines are parallel and cut by a transversal

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The measure of each numbered angle:- $\angle1, \: \angle2 \:and\: \angle3$

${\green{\underline{\underline{\bold{Solution:-}}}}}$

In the given figure,

$\angle3 = 120°$

Reason:-

They are vertically opposite angles

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$\angle1 = 180° - 140°\\ \\</p><p></p><p>\angle1 = 40°$

Reason:-

They are interior allied angles

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$\angle2 = 180°- \angle3 \\ \\</p><p></p><p>\angle2 = 180° - 120° \\ \\</p><p></p><p>\angle2 = 60°$

Reason:-

They are interior allied angles

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${\pink{\underline{\underline{\bold{Additional \:Information:-}}}}}$

When two parallel lines are interested by a transversal then:-

• Corresponding angles are equal

• Vertically opposite angles are equal

• Interior alternate angles are equal

• Exterior alternate angles are equal

• Sum of Adjacent angles is 180°

• Sum of interior allied angles is 180°

• Sum of exterior allied angles is 180°