Question

In the given figure, AB || CD and EF is a transversal. If angle8 = 110°,
find each one of the unknown angles, marked in the figure. Give
reasons.​

Answer 1

$\bf{\dag}\:\underline{\frak{QuestiOn\;:}}$

In the Given figure, AB || CD and EF is a transversal. If ∠8 = 110°. Find each one of the unknown angles, matked in the fig. Give reasons.

$\bf{\dag}\:\underline{\frak{AnswEr\::}}$

$\bigstar\underline{\textsf{ \: From\;fig. \;Line segment\;CD\:}}\\\twoheadrightarrow\sf \angle 7 + \angle 8 = 180^\circ\\\twoheadrightarrow\sf \angle 7 + 110^\circ = 180^\circ\\\twoheadrightarrow\sf \angle 7 = 180^\circ - 110^\circ\\\twoheadrightarrow\sf \angle 7 = 70^\circ\\\\\therefore\: \underline{\boxed{\sf \angle 7= 70^\circ}}\\\dfrac{\qquad\qquad \qquad\qquad\qquad\qquad\qquad}{}$

⇥ ∠1 = ∠4 (Vertically Opposite Angles)

⇥ ∠3 = ∠2 (Vertically Opposite Angles)

⇥ ∠5 = ∠8 (Vertically Opposite Angles)

⇥ ∠7 = ∠6 (Vertically Opposite Angles)

⇥ ∠1 = ∠5 (Corresponding Angles)

∴ Hence, ∠2, ∠3, ∠7 & ∠6 are 70° and ∠1, ∠4 & ∠5 are 110° respectively.

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D E F I N I T I O N S :

• Alternate Interior Angles: These angles are formed when two || and non || are intersected by any transversal.

• Vertically Opposite Angles: These angles are vertically Opposite from each other at any vertex as in attached figure ∠S = ∠O.

• Linear Pair Angles: When two lines Intersect each other at any single point then two pair of angles are called linear pair.

Answer 2

Answer :-

$\pink{\bigstar}$ Measure of each one of the unknown angles :-

• $\sf \angle{1}\:\leadsto\:{\boxed{\tt{\blue{110^{\circ}}}}}$

• $\sf \angle{2}\:\leadsto\:{\boxed{\tt{\blue{70^{\circ}}}}}$

• $\sf \angle{3}\:\leadsto\:{\boxed{\tt{\blue{70^{\circ}}}}}$

• $\sf \angle{4}\:\leadsto\:{\boxed{\tt{\blue{110^{\circ}}}}}$

• $\sf \angle{5}\:\leadsto\:{\boxed{\tt{\blue{110^{\circ}}}}}$

• $\sf \angle{6}\:\leadsto\:{\boxed{\tt{\blue{70^{\circ}}}}}$

• $\sf \angle{7}\:\leadsto\:{\boxed{\tt{\blue{70^{\circ}}}}}$

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• Given :-

• In the given figure, AB || CD and EF is a transversal and ∠8 = 110°.

• To Find :-

• Each one of the unknown angles, marked in the figure.

• Solution :-

➪ $\sf \angle{6} + \angle{8} = 180^{\circ}\:\quad(Linear \:pair)$

➪ $\sf \angle{6} + 110^{\circ} = 180^{\circ}$

➪ $\sf \angle{6} = 180^{\circ} - 110^{\circ}$

➪ $\sf \angle{6} = {\bf{\red{70^{\circ}}}}$

Now,

➪ $\sf \angle{8} = \angle{5} = {\bf{\red{110^{\circ}}}}\:(Vertically \:opposite\:\angle{'s})$

➪ $\sf \angle{7} = \angle{6} = {\bf{\red{70^{\circ}}}}\:(Vertically \:opposite\:\angle{'s})$

Also,

➪ $\sf \angle{5} = \angle{1} = {\bf{\red{110^{\circ}}}}\:(Corresponding\:\angle{'s})$

➪ $\sf \angle{7} = \angle{3} = {\bf{\red{70^{\circ}}}}\:(Corresponding\:\angle{'s})$

➪ $\sf \angle{8} = \angle{4} = {\bf{\red{110^{\circ}}}}\:(Corresponding\:\angle{'s})$

➪ $\sf \angle{6} = \angle{2} = {\bf{\red{70^{\circ}}}}\:(Corresponding\:\angle{'s})$

Hence,

• ∠2 = ∠3 = ∠6 = ∠7 = 70°
• ∠1 = ∠4 = ∠5 = 110°

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