Math, asked by Minico, 1 month ago

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.​

Attachments:

Answers

Answered by ShírIey
244

\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.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀

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.
Attachments:

BrainIyMSDhoni: Amazing :)
MasterDhruva: Perfect.
Answered by MяMαgıcıαη
202

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}}}}}

\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}

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°

\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3mm}\put(1,1){\line(1,0){6.8}}\end{picture}


BrainIyMSDhoni: Good :)
Similar questions