R d sharma solutions mathematics class 8 Solutions for Chapter 16 understanding shapes quadrilaterals

Define the following terms:

(i)Quadrilateral

(ii)Convex Quadrilateral

In a quadrilateral, define each of the following:

(i)Sides

(ii)Vertices

(iii)Angles

(iv)Diagonals

(v)Adjacent angles

(vi)Adjacent sides

(vii)Opposite sides

(viii)Opposite angles

(ix)Interior

(x)Exterior

Complete each of the following, so as to make a true statement:

(i)A quadrilateral hassides.

(ii)A quadrilateral hasangles.

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

(iv)A quadrilateral hasdiagonals.

(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 twovertices of the quadrilateral.

(ix)The sum of the angles of a quadrilateral isright angles.

(x)The measure of each angle of a convex quadrilateral is180°.

(xi)In a quadrilateral the point of intersection of the diagonals lies inof the quadrilateral.

(xii)A point is in the interior of a convex quadrilateral, if it is in theof its two opposite angles.

(xiii)A quadrilateral is convex if for each side, the remaininglie on the same side of the line containing the side.

In Fig. 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?

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

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

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

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

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

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

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

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

In Figure, find the measure of ∠MPN.

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

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

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.

In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that ∠COD = 1/2 (∠A +∠B).

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°

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

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

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.

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

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

PQRSTU is a regular hexagon, determine each angle of ΔPQT.