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Take four congruent card-board copies of any quadrilateral ABCD, with angles as shown [Fig 3.5 (i)]. Arrange the copies as shown in the figure, where angles ∠1, ∠2, ∠3, ∠4 meet at a point [Fig 3.5 (ii)]. What can you say about the sum

Q2. Take four congruent card-board copies of any quadrilateral ABCD, with angles as shown [Fig 3.5 (i)]. Arrange the copies as shown in the figure, where angles ∠1, ∠2, ∠3, ∠4 meet at a point [Fig 3.5 (ii)].

What can you say about the sum of the angles ∠1, ∠2, ∠3 and ∠4?

[Note: We denote the angles by ∠1, ∠2, ∠3, etc., and their respective measures by m∠1, m∠2, m∠3, etc.]

The sum of the measures of the four angles of a quadrilateral is___________.
You may arrive at this result in several other ways also.

Answers (1)
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As we know the sum of all four angles of a quadrilateral is360\degree.

\angle 1,\angle 2,\angle 3,\angle 4 are four angles of quadrilateral ABCD.

Hence, the sum of these angles is 360\degree = \angle 1+\angle 2+\angle 3+\angle 4

Angles ∠1, ∠2, ∠3, ∠4 meet at a point and sum of these angles is 360\degree = \angle 1+\angle 2+\angle 3+\angle 4.

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