NCERT Solutions for class 7 maths Chapter 5
In this section of, NCERT solutions for class 7 Maths chapter 5 lines and angles, we discuss about some basic properties of triangle. Which is given below, students can direct access from the given link.
Class 7 maths Chapter 5 Ex. 5.1
NCERT Solutions for Class 7 Maths Chapter 5 (Lines and Angles). Solution of this chapter is given in English medium. The student can direct access Exercise 5.1 and Exercise 5.2 here.
Class 7 Maths Chapter 5 Ex. 5.2
Solutions for Class 7 Maths Chapter 5 (Lines and Angles)Solution of this chapter is given in English medium. The student can direct access Exercise 5.1 and Exercise 5.2 here.
Definitions:
Acute angle : An angle from 0 degree to less than 90 degree , is called acute angle. For example 30 degree, 60 degree etc. are acute angles. All angles of an equilateral triangle are acute angle.
Right angle : An angle which is measured exactly 90 degree, is called right angle. In a square all angles are right angles and also in rectangle, all angles right angles.
Obtuse angle : An angle which is measured greater than 90 degree but less than 180 degree, is called obtuse angle. In a parallelogram, two angles out of four angles definitely will be obtuse angle.
Straight angle : An angle which is measured exact 180 degree, is called straight angle.
Reflex angle in NCERT solutions for class 7 Maths chapter 5 : An angle which is measured more than 180 degree but less than 360 degree, is called reflex angle.
Complete angle : An angle which is measured exact 360 degree is called complete angle. Complete angle formed on the centre of circle.
Complementry angle: When the sum of the measures of two angles is 90 degree , then the angle are called complementry angles. For example, if a angle measured θ degree then it’s complemenrty angle will be (90 – θ) degree . And also if the angle measured (90 – θ) degree then its complementry will be θ degree.
Questions related to complementry angles
1. Can two acute angles be complement to each other?
The answer is YES ! because it is known that the acute angle is less than 90 degree. So if we take an angle of 60 degree and other angle of 30 degree,(because these two angles are acute angle) then the sum of these two angles are 90 degree. Which is satisfy the definition of the complementry angle. Therefore the statement which is given in the question is right.
2. Can two obtuse angles be complement to each other?
The answer of this question is NO! Because it is known that the obtuse angle is greater than 90 degree but less than 180 degree. So if we take two obtuse angle measured 100 degree and 120 degree (Because both are obtuse angle) then the sum of both angles are (100 + 120) degree = 220 degree, which is greater than 90 degree. Which is not satify the definition of the complementry angles. Therefore the given statement in the question is wrong(impossible).
3. Can two right angles be complement to each other?
No! Because it is known that , the sum of measures of two angles is 90 degree, is called complementry angle. But if we take 2 right angle means 90 degree and 90 degree, then the sum of these angles is greater than 90 degree which not follow the definition of the complementry. Therefore the given statements in the question is not possible.
Supplementry angle: When the sum of the measures of two angles is 180 degree, then the angles are called supplementry angles. For exemple, if a angle measured x degree then it’s complemenrty angle will be (90 – x) degree . And also if the angle measured (90 – x) degree then its complementry will be x degree.
Questions related to supplementry angles
1. Can two obtuse angles be supplementary?
Answer of this question is NO ! because it is known that obtuse angle measured from greater than 90 degree but less than 180 degree. If we take two obtuse angle measured 100 degree and 120 degree (which is obtuse angle). Now if we add these two obtuse angles (100 + 120) degree = 220 degree .Then the sum is greater than 180 degree. Which is not satify the definition of the supplementry angle .Therefore the given statement in the question is not possible.
2. Can two acute angles be supplementary?
If we read the statement carefully, we will find that it is impossible.Because It is known that the measures of acute angle is less than 90 degree. For observation let we take two acute angles measured 60 degree and 80 degree (both are acute angles).Now if we add these two angle (60 +80 = 140 ) we find 140 degree, which is less than the supplementry angles. Which is not follow the definition of the supplementry angles. Therefore given statement in the question is not possible.
3. Can two right angles be supplementary?
Yes ! it is correct , it is possible. Let we take two right angles (obviously both are 90 degree) if we add them then we get ,90 + 90 = 180 degree. Which is satisfy the definition of the supplementry angles. Therefore given statement in the question is correct (possible).
- Adjacent angle : A pair of angles are placed next to each other. They are called adjacent angles if they are follow these conditions:
- (i) they have a common vertex,
- (ii) they have a common arm; and
- (iii) the non-common arms on either side of the common arm.
Such pairs of angles are called adjacent angles. Adjacent angles have a common vertex and a common arm but no common interior points.
Question related to adjacent angles
1. Can two adjacent angles be supplementary?
It is known that , if the sum of two angles is 180 degree then they are called supplementry angle. Now if we read the statement , then we find that if the sum of two adjacent angles is 180 degree. Then they are supplementry to each other, but if the sum is less than 180 degree then they are not supplementry to each other. For conclusion , the given statement in the question is possible.
2. Can two adjacent angles be complementary?
Yes ! it is possible. It is known that , if the sum of two angles is 90 degree then they are called complementry angle to each other. Now if we read the statement , then we find that if the sum of two adjacent angles is 90 degree. Then they are complementry to each other, but if the sum is less than 90 degree then they are not complementry to each other. For conclusion , the given statement in the question is possible.
3. Can two obtuse angles be adjacent angles?
Answer is May be, may be not .It is known that if both obtuse angles follow these adjacent angle’s conditions, i.e they have a common vertex, they have a common arm; and the non-common arms on either side of the common arm . Then both obtuse angles will be adjacent angle otherwise they are not adjacent angles.
4. Can an acute angle be adjacent to an obtuse angle?
Yes ! It is possible. In adjacent angles, any one of them will be acute angle or obtuse angle.
Question Related to linear pair
Linear Pair : A linear pair is a pair of adjacent angles whose non-common sides are opposite rays. If the sum of adjacent angles is 180 degree then they are linear pair otherwise they are not linear pair. An important fact is, all adjacent angles are not a linear pair.
Question related to adjacent angles in NCERT solutions for class 7 Maths chapter 5:
1. Can two acute angles form a linear pair?
Impossible ! it is know that, if the sum of adjacent angles are 180 degree then they are linear pair otherwise they are not linear pair. Now from above statements, we know that acute angle is less than 90 degree . If we take adjacent angles wich is measured acute angles (both). Then their sum will be less than 180 degree. Therefore two acute angles can not form a linear pair.
2. Can two obtuse angles form a linear pair?
We know that the obtuse angles is measured from greater than 90 degree but less than 180 degree. Now if we take two obtuse angle measured 100 degree and 120 degree, then the sum of these obtuse angle is (100 + 120 = 220) more than 180 degree . Which is more than linear pair (180 degree). Therefore given statement is not possible.
3. Can two right angles form a linear pair?
Obviously, Yes ! Because, if we add two right angles then we get 180 degree which is follow the linear pair condition. Therefore two right angles form a linear pair.
Vertically Opposite Angles: when two lines intersects to each other at a point, then vertically opposite angles are equal.
Transversal : If a line l intersects two another line at two different points then line l is called transversal line of both other line.
Facts related to transversal:
(i) If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal.
(ii) If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
(iii) If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary.
(iv) when a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.