Q3 of 9 Page 185

Prove that the sum of the angles of a quadrilateral is 360°.


ABCD is a quadrilateral and AC is a diagonal. Now, we get two triangles


∆ ABC and ∆ ACD.


As we know that sum of angles of triangle is 180°


So, sum of two triangles will be 180° × 2 = 360°


i.e. the sum of the angles of a quadrilateral is 360°

More from this chapter

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1

Fill in the blanks:

(i) A quadrilateral has ……………..sides.


(ii) A quadrilateral has……………. angles.


(iii) A quadrilateral has……………. vertices, no three of which are……………..


(iv) A quadrilateral has ……………..diagonals.


(v) A diagonal of a quadrilateral is a line segment that joins two………………. vertices of the quadrilateral.


(vi) The sum of the angles of a quadrilateral is ………………..

 2

In the adjoining figure, ABCD is a quadrilateral.

(i) How many pairs of adjacent sides are there? Name them.


(ii) How many pairs of opposite sides are there? Name them.


(iii) How many pairs of adjacent angles are there? Name them.


(iv) How many pairs of opposite angles are there? Name them.


(v) How many diagonals are there? Name them.


 4

The three angles of a quadrilateral are 76°, 54° and 108°. Find the measure of the fourth angle.

 5

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.