# Worksheets for angles and lines

1) XY is a straight line. Find the sum of ∠a, ∠b, ∠c, ∠d and ∠e.

Ans :- The sum is 320°

2) The diagram below shows a right angle triangle, PQR, not drawn to scale. Given that ∠TRQ = 15°, PS = SR and the ratio of ∠a : ∠b is 2 : 3, find ∠STR.

Ans :- ∠STR = 75°

3) In the figure below, DEF and DGC are straight lines. ABCD is a trapezium, CDE is an isosceles triangle and BCG is an equilateral triangle. Line AC is parallel to line DF.
(a) Find ∠CDE
(b) Find ∠BCA

Ans :- a) 35°
b) 25°

4) In the figure below, PQTU is a square, TUV is a equilateral triangle and RSTV is a rhombus. Find
(a) ∠QRS
(b) ∠PVQ

Ans :- a) ∠QRS =105°
b) ∠PVQ = 105° .

5)In the figure below, not drawn to scale, TUZA is a rhombus.
∠TUZ = 65° and ∠ZXY = 37°. Find ∠TYA.

Ans :- ∠TYA = 85.5°

6) In the figure below, PQRS, XRUW, YQT and TUV are straight lines and QRUT is a rhombus.
Find the value of ∠a + ∠b + ∠c + ∠d + ∠e + ∠f.

Ans :- value of ∠a + ∠b + ∠c + ∠d + ∠e + ∠f is 310°

7) In the diagram below, ABCD is a square and DE = EC = CD.
Find ∠AEB

Ans :- ∠AEB = 150°

8) The figure below is not drawn to scale. KLMN is a straight line. OL is parallel to PM. Find ∠LOK.

Ans :- ∠LOK = 22°

9) In the figure below, not drawn to scale, PQR is an equilateral triangle while WXYZ is a square. Find ∠k.

Ans :- ∠k = 20°

10) The figure below is not drawn to scale. ABEF is a rhombus and BCDE is a parellogram. ABC and DEF are straight lines. ∠CDE = 76° and ∠BED - ∠AEC = 27°.
Find
(a) ∠FAE
(b) ∠BEC

Ans :- (a) ∠FAE = 38°
(b) ∠BEC = 39°