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#### Question 1:

Define the following terms:

(i) A quadrilateral is a polygon that has four sides (or edges) and four vertices (or corners).
It can be any four-sided closed shape.

(ii) A convex quadrilateral is a mathematical figure whose every internal angle is less than or equal to 180 degrees.

#### Question 2:

In a quadrilateral, define each of the following:
(i) Sides
(ii) Vertices
(iii) Angles
(iv) Diagonals
(vii) Opposite sides
(viii) Opposite angles
(ix) Interior
(x) Exterior

#### Question 3:

Complete each of the following, so as to make a true statement:
(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) The number of pairs of adjacent angles of a quadrilateral is .......
(vi) The number of pairs of opposite angles of a quadrilateral is .......
(vii) The sum of the angles of a quadrilateral is ......
(viii) A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.
(ix) The sum of the angles of a quiadrilateral is .... right angles.
(x) The measure of each angle of a convex quadrilateral is ..... 180°.
(xi) In a quadrilateral the point of intersection of the diagonals lies in .... of the quadrilateral.
(xii) A point is in the interior of a convex quadrilateral, if it is in the ..... of its two opposite angles.
(xiii) A quadrilateral is convex if for each side, the remaining .... lie on the same side of the line containing the side.

(i) four
(ii) four
(iii) four, collinear
(iv) two
(v) four
(vi) two
(vii) 360°
(viii) opposite
(ix) four
(x) less than
(xi) the interior
(xii) interiors
(xiii) vertices

#### Question 4:

In Fig. 16.19, ABCD is a quadrilateral.
(i) Name a pair of adjacent sides.
(ii) Name a pair of opposite sides.
(iii) How many pairs of adjacent sides are there?
(iv) How many pairs of opposite sides are there?
(v) Name a pair of adjacent angles.
(vi) Name a pair of opposite angles.
(vii) How many pairs of adjacent angles are there?
(viii) How many pairs of opposite angles are there?

#### Question 5:

The angles of a quadrilateral are 110°, 72°, 55° and x°. Find the value of x.

#### Question 6:

The three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.

#### Question 7:

A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?

#### Question 8:

A quadrilateral has all its four angles of the same measure. What is the measure of each?

#### Question 9:

Two angles of a quadrilateral are of measure 65° and the other two angles are equal. What is the measure of each of these two angles?

#### Question 10:

Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.

#### Question 11:

The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.

#### Question 12:

If the sum of the two angles of a quadrilateral is 180°. What is the sum of the remaining two angles?

#### Question 13:

In Fig. 16.20, find the measure of ∠MPN.

#### Question 14:

The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?

#### Question 15:

In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C = 100° and ∠D = 50°, find the measure of ∠APB.

#### Question 16:

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.

#### Question 17:

In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that $\angle COD=\frac{1}{2}\left(\angle A+\angle B\right).$

#### Question 18:

Find the number of sides of a regular polygon, when each of its angles has a measure of
(i) 160°
(ii) 135°
(iii) 175°
(iv) 162°
(v) 150°

#### Question 19:

Find the number of degrees in each exterior exterior angle of a regular pentagon.

#### Question 20:

The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.

#### Question 21:

In a convex hexagon, prove that the sum of all interior angle is equal to twice the sum of its exterior angles formed by producing the sides in the same order.

#### Question 22:

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.

#### Question 23:

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.