CBSE Class 9 Mathematics Lines And Angles Worksheet Set 01

CBSE Class 9 Mathematics Worksheet  Lines and Angles - Practice worksheets for CBSE students. Prepared by teachers of the best CBSE schools in India.

ASSERTION & REASONING QUESTIONS

DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R).
Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion : If angles ‘a ’ and ‘b’ form a linear pair of angles and a = 40°, then b = 150°.
Reason : Sum of linear pair of angles is always 180°.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the sum of linear pair of angles is always 180°.
So, Reason is correct.
Now, a + b = 40° + 150° = 190° ≠180°
Hence, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5 : 4, then the greater of the two angles is 100°.
Reason : If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180°.
Answer : We know If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180° hat the solution of the line will satisfy the equation of the line.
So, Reason is correct.
Let the angles be 5x and 4x
Since, these two angles are co-interior angles. So, we
have 5x + 4x = 180° ⇒ 9x = 180° ⇒ x = 20°
Hence, greater angle = 5x = 5 x 20° = 100°
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : An angle is 140 more than its complementary angle, then angle is 520.
Reason : Two angles are said to be supplementary if their sum of measure of angles is 180°.
Answer : We know that two angles are said to be supplementary if their sum of measure of angles is 180°.
So, Reason is correct.
Let the angle be x . Complement of x = (90° - x)
Since, the difference is 140, we have x – (90° – x) = 140
⇒ 2x = 104°
⇒ x = 52°
So, Assertion is also correct
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : Supplement of angle is one fourth of itself. The measure of the angle is 1440.
Reason : Two angles are said to be supplementary if their sum of measure of angles is 180°.
Answer : We know that two angles are said to be supplementary if their sum of measure of angles is 180°.
So, Reason is correct.
Let the angle be x . Supplement of x = (1/4) x
So, x + 1/2 x = 180°  ⇒ (5/4) x = 180° ⇒ x = 144°
So, Assertion is also correct 
Also, reason (R) is the correct explanation of assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion: The value of x from the adjoining figure, if l || m is 150.
Reason: If two parallel lines are intersected by a transversal, then each pair of corresponding angles so formed is equal.
Answer : We know that If two parallel lines are intersected by a transversal, then each pair of corresponding angles so formed is equal.
So, Reason is correct.
Also, we know that If a transversal intersects two parallel lines, then the sum of the interior angles on the same side of the transversal is 180°.
From figure we have, 120° – x + 5x = 180°
⇒ 4x = 180° – 120°
⇒ 4x = 60°
⇒ x = 15°
So, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : If two internal opposite angles of a triangle are equal and external angle is given to be 110°, then each of the equal internal angle is 55°.
Reason : A triangle with one of its angle 900, is called a right triangle.
Answer : For Assertion: We know that the exterior angle is equal to the sum of its interior opposite angles. So, x + x = 110°.
⇒ 2x = 110°
⇒ x = 55°
So, Assertion is correct
Also, we know that a triangle with one of its angle 900, is called a right triangle.
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : Sum of the pair of angles 120° and 60° is supplementary.
Reason : Two angles, the sum of whose measures is 180°, are called supplementary angles.
Answer : We know that two angles are said to be supplementary if their sum of measure of angles is 180°.
So, Reason is correct.
Now, 120° + 60° = 180° ⇒ Sum of the pair of angles 120° and 60° is supplementary.
So, Assertion is also correct
Also, reason (R) is the correct explanation of assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : A triangle can have two obtuse angles.
Reason : The sum of all the interior angles of a triangle is 180°
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the sum of all the interior angles of a triangle is 180°.
So, Reason (R) is true.
Since the Sum of two obtuse angles will be more than 180°.
So, Assertion (A) is false.
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle of the triangle is 800.
Reason: The sum of all the interior angles of a triangle is 180°
Answer : We know that the sum of all the interior angles of a triangle is 180°.
So, Reason (R) is true.
Let the angles of a triangle be 2x, 3x and 4x then we have
2x + 3x + 4x = 180°
⇒ 9x = 180°
⇒ x = 20°.
Hence, Largest angle = 4 x 20° = 80°.
So, Assertion (A) is also true.
Also, Reason (R) is a correct explanation of Assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion: In the given figure, AOB is a straight line. If ∠AOC = (3x + 10) ° and ∠BOC (4x − 26) °, then ∠BOC = 860
Reason: The sum of angles that are formed on a straight line is equal to 180°.
Answer : We know that the sum of angles that are formed on a straight line is equal to 180°.
So, Reason is correct
We have : ∠AOC+∠BOC=180° [Since AOB is a straight line ]
⇒3x + 10 + 4x − 26 = 180°
⇒7x = 196°
⇒x = 28°
∴∠BOC = [4 × 28 − 26]°
⇒∠BOC=86°.
So, Assertion (A) is also true.
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .

Question. Assertion : The angles of a triangle are in the ration 3 : 5 : 7. The triangle is acuteangled
Reason : The sum of angles that are formed on a straight line is equal to 180°.
Answer : We know that the sum of angles that are formed on a straight line is equal to 180°.
So, Reason is correct
Also, the sum of all the interior angles of a triangle is 180°
Let the angles measure (3x) °, (5x) ° and (7x) °.
Then,3x + 5x + 7x = 180°   ⇒15x = 180° ⇒x = 12°
Therefore, the angles are 3(12) °=36°, 5(12) °= 60° and 7(12) ° = 84°.
Hence, the triangle is acute-angled.
So, Assertion (A) is also true.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Students must free download and practice these worksheets to gain more marks in exams. CBSE Class 9 Mathematics Worksheet  Lines and Angles