Question

identify the following figure..
(1) Write the pair of corresponding angles.
(11) The pair of alternate Interior angles.
(III) The pair of Interior angles on same side of transversal.
(iv) The opposite vertically opposite angles.
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Answer 1

Hi mate......✌✌

Greetings to u !!

here is ur answer ⬇

According to the given figure,

(1) Pairs of corresponding angles -

• ∠1 and ∠5

• ∠4 and ∠8

• ∠2 and ∠6

• ∠3 and ∠7

(2) Pairs of alternate interior angles -

• ∠2 and ∠8

• ∠3 and ∠5

(3) Pair of angles on the same side of transversal or Cointerior angles -

• ∠2 and ∠5

• ∠3 and ∠8

(4) Pair of vertically opposite angles -

• ∠1 and ∠3
• ∠2 and ∠4
• ∠5 and ∠7
• ∠6 and ∠8

✍ Some more to know :-

☆ Whenever a pair of parallel lines is intersected by a transversal,

• corresponding angles are equal
• alternate interior angles are equal
• sum of cointerior angles is supplementary i.e, 180°

→ Corresponding Angles

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles.

for e,g :- ∠1 and ∠5  ;  ∠4 and ∠8

→ Alternate interior angles

These are angles that are in opposite positions relative to a transversal intersecting two lines.

for e,g :-  ∠2 and ∠8  ;   ∠3 and ∠5

→ Cointerior angles / Allied angles

These angles lie between two lines and on the same side of a transversal.

for e.g :- ∠2 and ∠5  ;  ∠3 and ∠8

Hope it helps ✨

Answer 2

Step-by-step explanation:

Given: The corresponding image for the figure.

To Find: (1)The pair of corresponding angles.

(II) The pair of alternate Interior angles.

(III) The pair of Interior angles on same side of transversal.

(IV) The opposite vertically opposite angles.

• We know, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections of the transversal. In the figure, the pair of corresponding angles are:

        $\angle4\ and\ \angle 8\\\angle3\ and\ \angle 7\\\angle1\ and\ \angle 5\\\angle2\ and\ \angle 6$

• The angles that lie on the inner side of the parallel lines but on the opposite sides of the transversal are known as the alternate interior angles. In the figure, the pair of alternate interior angles are:

        $\angle3\ and\ \angle 5\\\angle2\ and\ \angle 8$

• The angles that lie on the inner side of the parallel lines and on the same sides of the transversal are as follows:

       $\angle3\ and\ \angle 8\\\angle2\ and\ \angle 5$

• The Vertically opposite angles are a pair of non-adjacent angles formed when two lines intersect. Here, the pair of vertically opposite angles are:

       $\angle4\ and\ \angle 2\\\angle1\ and\ \angle 3\\\angle5\ and\ \angle 7\\\angle8\ and\ \angle 6$