NCERT Solutions for class 8 math chapter 3 ex 3.1
Keeping the examination point of view in mind the mathematicsandinformationtechnology.com team has prepared NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals. The NCERT Solutions for chapter Understanding Quadrilaterals solutions explains the easy and simple way to solve the problems. By understanding these ways in NCERT Solutions for Class 8, students will be confident while solving such problems found in Chapter 3 Understanding Quadrilaterals.
Given here are some figures.
Classify each of them on the basis of the following.
(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon
Answer:
(a) 1, 2, 5, 6, 7
(b) 1, 2, 5, 6, 7
(c) 1, 2
(d) 2
(e) 1
How many diagonals does each of the following have?
Answer:
What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Answer:
The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.
Here, ABCD is a convex quadrilateral, made of two triangles △ABD and△BCD.
Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e.,
180º + 180º = 360º
Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.
Here again, ABCD is a concave quadrilateral, made of two triangles △ABD and △ BCD.
Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º.
Question 4:
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
(a) 7
(b) 8
(c) 10
(d) n
Answer:
From the table, it can be observed that the angle sum of a convex polygon of n sides is (n −2) × 180º.
Hence, the angle sum of the convex polygons having number of sides as above will be as follows.
(a) (7 − 2) × 180º = 900°
(b) (8 − 2) × 180º = 1080°
(c) (10 − 2) × 180º = 1440°
(d) (n − 2) × 180°
What is a regular polygon? State the name of a regular polygon of
Answer:
A polygon with equal sides and equal angles is called a regular polygon.
Find the angle measure x in the following figures.
Answer:
(a)
Sum of the measures of all interior angles of a quadrilateral is 360º. Therefore, in the given quadrilateral,
50° + 130° + 120° + x = 360°
300° + x = 360°
x = 60°
(b)
From the figure, it can be concluded that,
90º + a = 180º (Linear pair)
a = 180º − 90º = 90º
Sum of the measures of all interior angles of a quadrilateral is 360º.
Therefore, in the given quadrilateral,
60° + 70° + x + 90° = 360°
220° + x = 360°
x = 140°
(c)
From the figure, it can be concluded that,
70° + a = 180° (Linear pair)
a = 110°
60° + b = 180° (Linear pair)
b = 120°
Sum of the measures of all interior angles of a pentagon is 540º.
Therefore, in the given pentagon,
120° + 110° + 30° + x + x = 540°
260° + 2x = 540°
2x = 280°
x = 140°
(d)
Sum of the measures of all interior angles of a pentagon is 540º.
5x = 540°
x = 108°
a)Find x+y+z
Answer:
(a) x + 90° = 180° (Linear pair)
x = 90°
z + 30° = 180° (Linear pair)
z = 150°
y = 90° + 30° (Exterior angle theorem)
y = 120°
x + y + z = 90° + 120° + 150° = 360°
(b)
Sum of the measures of all interior angles of a quadrilateral is 360º. Therefore, in the given quadrilateral,
a + 60° + 80° + 120° = 360°
a + 260° = 360°
a = 100°
x + 120° = 180° (Linear pair)
x = 60°
y + 80° = 180° (Linear pair)
y = 100°
z + 60° = 180° (Linear pair)
z = 120°
w + 100° = 180° (Linear pair)
w = 80°
Sum of the measures of all interior angles = x + y + z + w
= 60° + 100° + 120° + 80°
= 360°
