Q2 =>
Angles between South
between South and West and
South and East are
(a) vertically opposite angels
(b) complementary angles
(d) adjacent but not supplementary
(e) making a linear pair
Answers
Answer:
The angles between North and West and South and East are
(a) complementary (b) supplementary
(c) both are acute (d) both are obtuse
Solution :
From the above figure, it is clear that the angle between North and West is 90° and
South and East is 90°.
∴ Sum of these two angles = 90° + 90° = 180°
Hence, the two angles are supplementary, as their sum is 180°.
Question 2:
Angles between South and West and South and East are
(a) vertically opposite angles (b) complementary angles
(c) making a linear pair (d) adjacent but not supplementary
Solution :
From the above figure, we can say that angle between South and West is 90° and
angle between South and East is 90°. So, their sum is 180°.
Hence, both angles make a linear pair.
Question 3:
In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ABC = 46°, then ∠ABP is equal to
Solution :
(b) We know that, the angle of incidence is always equal to the angle of reflection.
Question 4:
If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
Solution :
(b) Let the angle be x°. Then, the complement of x will be (90 – x)°.
Given, complement of x° is 79°.
∴ (90 – x)°= 79°
⇒ x° = 90° – 79°= 11°
Therefore, the required angle is 11°.
Note Sum of the complementary angles is 90°.
Question 5:
Angles, which are both supplementary and vertically opposite are
(a) 95°, 85° (b) 90°, 90°
(c) 100°, 80° (d) 45°, 45°
Solution :
(b) Two angles are said to be supplementary, if their sum is 180°. Also, if two angles are vertically opposite, then they are equal.
Therefore, angles given in option (b) are supplementary as well as vertically opposite.
Question 6:
The angle which makes a linear pair with an angle of 61°, is of
(a) 29° (b) 61 °
(c) 122° (d) 119°
Solution :
(d) Let the required angle be x°. It is given that x° makes a linear pair with 61°.
∴ x + 61° = 180° [∴ sum of angles forming linear pair is 180°]
⇒ x = 180° – 61°= 119°
Question 7:
The angles x and 90°- x are
(a) supplementary (b) complementary
(c) vertically opposite (d) making a linear pair
Solution :
(b) Sum of the given angles = x + 90° – x = 90°
Since, the sum of given two angles is 90°.
Hence, they are complementary to each other.
Question 8:
The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
Solution :
(d) Sum of the given angles
= (x – 10°)+ (190° – x)= x -10° + 190° – x
= (x-x) + (190°-10°)=0 + 180°= 180°
Since, the sum of given angles is 180°, Hence, they are supplementary.
Question 9:
In the given figure, the value of x is
Solution :
(d) We know that, the sum of all angles around a point is 360°.
∴ 100°+46°+64°+x = 360°
⇒ 210°+ x = 360°
⇒ x = 360° -210°
⇒ x = 150°
Question 10:
In the given figure, if AB||CD, ∠APQ = 50° and ∠PRD = 130°, then ∠QPR is
Solution :
(c) Since, AB and CD are parallel and PR is a transversal.
Question 11:
In the given figure, lines l and m intersect each other at a point. Which of the following is false?
Solution :
(d) From the given Figure it is clear that, ∠a = ∠b and ∠c= ∠d
Question 12:
If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is
(a) 120° (b) 60° (c) 30° (d) 20°
Solution :
(a) It is given that, angles P and 0 are supplementary. Hence, the sum of P and O will be 180°
Question 13:
In the given figure, POR is a line. The value of a is
Solution :
(a) Since, POR is a line. So,
Answer:
The angles between North and West and South and East are
(a) complementary (b) supplementary
(c) both are acute (d) both are obtuse
Solution :
From the above figure, it is clear that the angle between North and West is 90° and
South and East is 90°.
∴ Sum of these two angles = 90° + 90° = 180°
Hence, the two angles are supplementary, as their sum is 180°.
Question 2:
Angles between South and West and South and East are
(a) vertically opposite angles (b) complementary angles
(c) making a linear pair (d) adjacent but not supplementary
Solution :
From the above figure, we can say that angle between South and West is 90° and
angle between South and East is 90°. So, their sum is 180°.
Hence, both angles make a linear pair.
Question 3:
In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. If ∠ABC = 46°, then ∠ABP is equal to
Solution :
(b) We know that, the angle of incidence is always equal to the angle of reflection.
Question 4:
If the complement of an angle is 79°, then the angle will be of
(a) 1° (b) 11°
(c) 79° (d) 101°
Solution :
(b) Let the angle be x°. Then, the complement of x will be (90 – x)°.
Given, complement of x° is 79°.
∴ (90 – x)°= 79°
⇒ x° = 90° – 79°= 11°
Therefore, the required angle is 11°.
Note Sum of the complementary angles is 90°.
Question 5:
Angles, which are both supplementary and vertically opposite are
(a) 95°, 85° (b) 90°, 90°
(c) 100°, 80° (d) 45°, 45°
Solution :
(b) Two angles are said to be supplementary, if their sum is 180°. Also, if two angles are vertically opposite, then they are equal.
Therefore, angles given in option (b) are supplementary as well as vertically opposite.
Question 6:
The angle which makes a linear pair with an angle of 61°, is of
(a) 29° (b) 61 °
(c) 122° (d) 119°
Solution :
(d) Let the required angle be x°. It is given that x° makes a linear pair with 61°.
∴ x + 61° = 180° [∴ sum of angles forming linear pair is 180°]
⇒ x = 180° – 61°= 119°
Question 7:
The angles x and 90°- x are
(a) supplementary (b) complementary
(c) vertically opposite (d) making a linear pair
Solution :
(b) Sum of the given angles = x + 90° – x = 90°
Since, the sum of given two angles is 90°.
Hence, they are complementary to each other.
Question 8:
The angles x – 10° and 190° – x are
(a) interior angles on the same side of the transversal
(b) making a linear pair
(c) complementary
(d) supplementary
Solution :
(d) Sum of the given angles
= (x – 10°)+ (190° – x)= x -10° + 190° – x
= (x-x) + (190°-10°)=0 + 180°= 180°
Since, the sum of given angles is 180°, Hence, they are supplementary.
Question 9:
In the given figure, the value of x is
Solution :
(d) We know that, the sum of all angles around a point is 360°.
∴ 100°+46°+64°+x = 360°
⇒ 210°+ x = 360°
⇒ x = 360° -210°
⇒ x = 150°
Question 10:
In the given figure, if AB||CD, ∠APQ = 50° and ∠PRD = 130°, then ∠QPR is
Solution :
(c) Since, AB and CD are parallel and PR is a transversal.
Question 11:
In the given figure, lines l and m intersect each other at a point. Which of the following is false?
Solution :
(d) From the given Figure it is clear that, ∠a = ∠b and ∠c= ∠d
Question 12:
If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is
(a) 120° (b) 60° (c) 30° (d) 20°
Solution :
(a) It is given that, angles P and 0 are supplementary. Hence, the sum of P and O will be 180°
Question 13:
In the given figure, POR is a line. The value of a is
Solution :
(a) Since, POR is a line. So,
Step-by-step explanation:
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