06. Worksheet Solutions: Lines & Angles

Multiple Choice Questions

Q1: Find the value of x(a) 98º

(b) 100º

(c) 108º

(d)96º

Ans: (c)

x + 36 + 36 = 180 ⇒ x = 108º

Q2: A pair of angles is called linear pair if the sum of two adjacent angles is?

(a) 180º

(b) 90º

(c) 270º

(d) 360º

Ans: (a)

Q3: Find the value of x, y and z

(a) x = 110º , y = 70º, z = 80º(b) x = 70º , y = 110º, z = 60º(c) x = 70º, y = 100º, z = 70º(d) x = 70º, y = 110º, z = 70º

Ans: (d)

Vertically opposite angle theorem and linear pair axiom can be used to find the answer

Q4: An exterior angle of the triangle is 110º. And its two opposite interior angles are in the ratio 5:6. What are the values of those angles?

(a) 50º, 60º

(b) 25º, 30º

(c) 35º, 42º

(d) 40º, 48º

Ans: (a)

Q5: Lines l || k and m || n. Find the value of angle z(a) 45º

(b) 60º

(c) 70º

(d) 50º

Ans: (b)

Q6:Find the value of x(a) 67º(b) 71º(c) 57º(d) None of these

Ans: (a)

Q7: The side BC, AB and AC of the triangle ABC are produced in order forming exterior angles ∠ACD = x, ∠BAE = y and ∠CBF = z then the value of 2x + 2y + 2z is

(a) 180°

(b) 360°

(c) 540°

(d) 720°

Ans: (d)

Let a, b,c be the angles of triangle, then a + b + c = 180Now x = a + b, y = b + c, z = a + cTherefore 2x + 2y + 2z = 4(a + b + c) = 720

Q8: The angles of the triangles are in the ratio 1 : 2 : 3. Then the triangle is

(a) scalene

(b) obtuse angled

(c) acute angled

(d) right angles

Ans: (d)

Let x, 2x, 3x be the angles of triangle, then x + 2x + 3x = 180Therefore x = 30So angles are 30, 60 and 90

True or False

Q1: Pairs of vertically opposite angles is always equal

Ans: True

Q2: The sum of the angles of a triangle is 180º

Ans: True

Q3: If the sum of two adjacent angles is 45º, then two adjacent angles are acute angles

Ans: True

Q4: If a line is perpendicular is one of two parallel lines, then it is also perpendicular to the other

Ans: True

Q5: Two lines are intersected by the transversal, and then the corresponding angles are equal

Ans: False

Q6: Can we have a triangle where all the interior angles are more than 60º

Ans: False

Q7: Sum of two complimentary angles is equal to 90º

Ans: True

Q8: Sum of all the exterior angles of any polygon is always 360º

Ans: True

Fill in the blanks 

Q1: Sum of two supplementary angles is ______.

Ans: 180º

Q2: Two lines parallel to the same line is ____ each other.

Ans: parallel

Q3: An acute angle is always less than _____.

Ans: 90º

Q4: Angles forming a linear pair are ______.

Ans: supplementary

Q5: If one angle of triangle is equal to the sum of other two angles, then the triangle is ______.

Ans: right angle triangle

Q6: If two straight lines intersect, the adjacent angles are ______.

Ans: supplementary

Table Type Question

Ans: Complementary = 90 − xSupplementary = 180 − x

Short Answer Type Questions

Q: Write the type of angles

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii) 

Ans:

(i) Acute angle

(ii) Right angle

(iii) Obtuse angle

(iv) Straight angle

(v) Reflex angle

(vi) Vertically opposite angle

(vii) Alternate interior angles