SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE

Subject: Mathematics STD VIII Div: __ Name: ________

Hints - Lines and Angles worksheet

1. Find the values of x, y and z in the following figure

2. Find the angle which is half of its complement.

3. If two supplementary angles are in the ratio 2 : 3 then find the angles.

Let the angles be 2x and 3x. Then, 2x + 3x = 1800 (Supplementary angles)

5x = 1800

X = 36

The angles are 2 x 36 and 3 x 36

i.e. 720 and 1080

4. In the diagram given below if PQ || ST then find the value of <T ?

x + x + 50 = 1800 (Linear pair)

2x + 50 = 1800

2x = 1300 x = 650

S = 400 (Q and S are Alternate angles)

5. Find the values of the variables in the figures given below?

a)

Construct a line parallel to PQ and RS

4x – 10 + 3x + 3 = 91 (since 4x – 10 and 3x + 3 are corresponding angles for the given

4x – 10 and 3x + 3 angles respectively)

7x – 7 = 91; 7x = 98; x = 98 ÷7 = 14

b)

a= 900 + 300 (Corresponding angles)

a = 1200

Sum of all the angles at D = 3600 (Angle at a point)

b = 360 – (90 + 90 + 30) = 360 – 210 = 1500

8. If AB || CD then find the value of X + Y

9. Observe the adjoining figure and answer the following with reasons.

a) Is AB || CD b) Is AB || EF

a) Yes. AB || CD (Because alternate angles

are equal)

b) Yes. AB || EF (Because the sum of co

interior angles = 1800)

10. Use the figure below to answer the following questions:

1. If x || y and Z is a Transversal, what can you say about the types of angles given

below?

a) Pairs of angles that are boxed b) One boxed and one unboxed angle

2. If <A = 20 - 2m and <D = m - 130 what is the value of m?

2. 20 -2m = m – 130 (Vertically opposite angles)

3m = 150

m= 50