NCERT Solutions for Class 8 Maths Chapter 16 Understanding Shapes II (Quadrilaterals) are provided here with simple step-by-step explanations. These solutions for Understanding Shapes II (Quadrilaterals) are extremely popular among class 8 students for Maths Understanding Shapes II (Quadrilaterals) Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of class 8 Maths Chapter 16 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NCERT Solutions. All NCERT Solutions for class 8 Maths are prepared by experts and are 100% accurate.
Page No 16.15:
Question 1:
Define the following terms:
(i) Quadrilateral
(ii) Convex Quadrilateral
Answer:
(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.
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Question 2:
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
Answer:
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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.
Answer:
(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
Page No 16.16:
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?
Answer:
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Question 5:
The angles of a quadrilateral are 110°, 72°, 55° and x°. Find the value of x.
Answer:
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Question 6:
The three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.
Answer:
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Question 7:
A quadrilateral has three acute angles each measures 80°. What is the measure of the fourth angle?
Answer:
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Question 8:
A quadrilateral has all its four angles of the same measure. What is the measure of each?
Answer:
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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?
Answer:
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Question 10:
Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.
Answer:
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Question 11:
The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.
Answer:
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Question 12:
If the sum of the two angles of a quadrilateral is 180°. What is the sum of the remaining two angles?
Answer:
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Question 13:
In Fig. 16.20, find the measure of ∠MPN.
Answer:
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Question 14:
The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?
Answer:
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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.
Answer:
Page No 16.17:
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.
Answer:
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Question 17:
In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that
Answer:
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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°
Answer:
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Question 19:
Find the number of degrees in each exterior exterior angle of a regular pentagon.
Answer:
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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.
Answer:
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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.
Answer:
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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.
Answer:
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Question 23:
Determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.
Answer:
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Question 24:
PQRSTU is a regular hexagon. Determine each angle of ΔPQT.
Answer:
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