## NCERT Solutions for class 7 Maths Chapter 5: Lines and Angles## Exercise 5.1
Here, the given angle is of 20°. Let the complement angle be A. A + 20° = 90° A = 90° - 20° A = 70° Thus, the complement angle is 70°.
Here, the given angle is of 63°. Let the complement angle be A. A + 63° = 90° A = 90° - 63° A = 27° Thus, the complement angle is 27°.
Here, the given angle is of 57°. Let the complement angle be A. A + 57° = 90° A = 90° - 57° A = 33° Thus, the complement angle is 33°.
Here, the given angle is of 105°. Let the supplement angle be A. A + 105° = 180° A = 180° - 105° A = 75° Thus, the supplement angle is 75°.
Here, the given angle is of 87°. Let the supplement angle be A. A + 87° = 180° A = 180° - 87° A = 93° Thus, the supplement angle is 93°.
Here, the given angle is of 154°. Let the supplement angle be A. A + 154° = 180° A = 180° - 154° A = 26° Thus, the supplement angle is 26°.
The given angles are 65° and 115°. Sum = 65° + 115° Sum = 180° Thus, the given angles are
The given angles are 63° and 27°. Sum = 63° + 27° Sum = 90° Thus, the given angles are
The given angles are 112° and 68°. Sum = 112° + 68° Sum = 180° Thus, the given angles are
The given angles are 130° and 50°. Sum = 130° + 50° Sum = 180° Thus, the given angles are
The given angles are 45° and 45°. Sum = 45° + 45° Sum = 90° Thus, the given angles are
The given angles are 80° and 10°. Sum = 80° + 10° Sum = 90° Thus, the given angles are
Let the angle be A. The complement equal to the angle will also be A. A + A = 90° 2A = 90° A = 90°/2 A = 45° Thus, the angle equal to its complement will be 45°.
Let the angle be A. The complement equal to the angle will also be A. A + A = 90° 2A = 90° A = 90°/2 A = 45° Thus, the angle equal to its supplement will be of 90°.
For example, ∠1 = 110° ∠2 = 70° Now, let's decreases the value of the ∠1 by 10°. ∠1 = 100° The value of angle 2 will be: 180° - ∠1 = 180° - 100° = 80° It shows that the decrease in the value of ∠1 results in the increase of the value of ∠2.
Acute angle is the angle less than 90 degrees. If the two angles are acute, their sum would be less than 180 degrees. Hence, we cannot define them as the supplementary angles. For example, ∠1 = 60° ∠2 = 72° Both of the angles are acute. Sum = ∠1 + ∠2 Sum = 60° + 72° Sum = 132° The sum of the given angles is less than 180°. Thus, the two angles cannot be supplementary if both of them are acute.
Obtuse angle is the angle between 90 degrees and 180 degrees. If the two angles are obtuse, their sum would be greater than 180 degrees. Hence, we cannot define them as the supplementary angles. For example, ∠1 = 160° ∠2 = 120° Both of the angles are obtuse. Sum = ∠1 + ∠2 Sum = 160° + 120° Sum = 280° The sum of the given angles is greater than 180°. Thus, the two angles cannot be supplementary if both of them are obtuse.
Right angle is the angle of 90 degrees. For example, ∠1 = 90° ∠2 = 90° Both of the angles are right. Sum = ∠1 + ∠2 Sum = 90° + 90° Sum = 180° The sum of the given angles is equal to 180°. Thus, the two angles are supplementary if both of them are right angles.
Let the given angle be 50° and the other angle be A. It is greater than 45°. A + 50° = 90° A = 90° - 50° A = 40° It is less than 45°. Thus, if one angle is greater than 45°, the other complement angle will be less than 45°.
- It has a common vertex.
- It has a common arm.
- The non-common arms are on either side of the common arm.
OR The angles of a linear pair have the sum equal to 180°. It means, ∠COE and ∠EOD =180°
The angles ∠BOD and ∠DOA lies on a straight line. Thus, their sum would be 180°.
∠COB is the vertically opposite angle of ∠5.
∠1 and ∠2 does not have a common vertex. Thus, it cannot be termed as the adjacent angles.
- It has a common vertex.
- It has a common arm.
- The non-common arms are on either side of the common arm.
So,
Angle y and 55° are supplementary angles. ∠y + 55° = 180° ∠y = 180° - 55°
Angle z is the vertically opposite angle to 125°. These angles are generally equal to each other. So,
(ii)
So,
Angle y and z are supplementary angles. ∠y + ∠z° = 180° ∠y + 40° = 180° ∠y = 180° - 40°
Angle y is the vertically opposite angle to 'x + 25°'. These angles are generally equal to each other. So, ∠y =x + 25° ∠y = 140° x + 25° = 140° x = 140° - 25°
(i) If two angles are complementary, then the sum of their measures is
(ii) If two angles are supplementary, then the sum of their measures is
(iii) Two angles forming a linear pair are
(iv) If two adjacent angles are supplementary, they form a
(v) If two lines intersect at a point, then the vertically opposite angles are always
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles is acute angles, then the other pair of vertically opposite angles are
## Exercise 5.2
- Present on different vertices
- Present on the same side of the transversal
- Are in the corresponding positions relative to the two lines
- Present on different vertices
- Present on the opposite side of the transversal
- Lies between the two lines
- Present on different vertices
- Present on the same side of the transversal
- Are in the corresponding positions relative to the two lines
Thus,
b and d are vertically opposite angles. So,
a and b are the supplementary angles. a + b = 180° a = 180° - b a = 180° - 125°
a and c are vertically opposite angles. So,
d and angle f are the corresponding angles, which are equal. Thus,
e and angle a are the corresponding angles, which are equal. Thus,
x + 110 = 180° x = 180° - 110°
Thus,
So, ∠DGC =70°
So, ∠DEF =70°
126° + 44° = 170° It is not equal to 180°. Hence, l is not parallel to m.
So, A = 180° - 75° A = 105° Angle A and 105° are the corresponding angles. According to the property, the corresponding angles are equal. But, the angles A and 105° are not equal. Hence, l is not parallel to m.
So, A = 180° - 123° A = 57° Angle A and 57° are the corresponding angles. According to the property, the corresponding angles are equal. Hence, l is parallel to m. iv.
So, A = 180° - 98° A = 82° Angle A and 72° are the corresponding angles. According to the property, the corresponding angles are equal. But, the angles A and 72° are not equal. Hence, l is not parallel to m. |