Selina solutions concise mathematica class 7 icse Solutions for Chapter 14 lines and angles including construction of angles

Q1) State, true or false :

(i) A line segment 4 cm long can have only 2000 points in it.

(ii) A ray has one end point and a line segment has two end-points.

(iii) A line segment is the shortest distance between any two given points.

(iv) An infinite number of straight lines can be drawn through a given point.

(v) Write the number of end points in

(a) a line segment AB (b) array AB

(c) a lineAB

(vi) Out of \overline{AB},\overrightarrow{AB,}\ \ \ \overline{AB,}\ \ \ and\ \overline{\ AB} which one has a fixed length?

(vii) How many rays can be drawn through a fixed point O?

(viii) How many lines can be drawn through three

(a) collinear points?

(b) non-collinear points?

(ix) Is 40° the complement of 60°?

(x) Is 45° the supplement of 45°?

Q2) In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Give, in each case, the reason for your answer.

Q3) In the given figure, B AC is a straight line.

Find : (i) x (ii) ∠AOB (iii) ∠BOC

Q4) Find y in the given figure.

Q5) In the given figure, find ∠PQR

Q6) In the given figure. p° = q° = r°, find each.

Q7) In the given figure, if x = 2y, find x and y

Q8) In the adjoining figure, if b° = a° + c°, find b.

Q9) In the given figure, AB is perpendicular to BC at B.

Find : (i) the value of x.

(ii) the complement of angle x.

Q10) Write the complement of:

(i) 25^{\circ}

(ii) 90^{\circ}

(iii) a^n

(iv) \left(x+5\right)^{\circ}

(v) \left(30-a\right)^{\circ}

(vi) \frac{1}{2} of a right angle

(vii) \frac{1}{3}of\ 180^{\circ}

(viii) 21^{\circ}17′

Q11) (i) 100°

(ii) 0°

(iii) x°

(iv) (x + 35)°

(v) (90 +a + b)° f

(vi) (110 – x – 2y)°

(vii) \frac{1}{5}\ ofa\ right\ angle

(viii) 80° 49′ 25″

Q12) (i) 10° and 80°

(ii) 37° 28′ and 52° 33′

(iii) (x+ 16)°and(74-x)°

(iv) 54°and\ \frac{2}{5}ofa\ right\ angle.

Q13) Are the following pairs of angles supplementary?

(i) 139^{\circ}\ \ \ and\ 39^{\circ}

(ii) 26^{\circ}59’\ \ and\ 153^{\circ}1′

(iii) \frac{3}{10}\ \ of\ a\ right\ angle\ and\ \frac{4}{15}of\ two\ right\ angles\

(iv) 2x^{\circ}+65^{\circ}\ \ and\ 115^{\circ}-2x^{\circ}

Q14) If 3x + 18° and 2x + 25° are supplementary, find the value of x.

Q15) If two complementary angles are in the ratio 1:5, find them.

Q16) If two supplementary’ angles are in the ratio 2 : 7, find them.

Q18) 20% of an angle is the supplement of 60°. Find the angle.

Q19) 10% of x° is the complement of 40% of 2x°. Find x .

Q20) Use the adjacent figure, to find angle x and its supplement.

Q21) Find k in each of the given figures.

Q22) In the given figure, lines PQ, MN and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR

Q23) In the given figure, find ∠AOB and ∠BOC.

Q24) Find each angle shown in the diagram.

Q25) AB, CD and EF are three lines intersecting at the same point.

(i) Find x, if y = 45° and z = 90°.

(ii) Find a, if x = 3a, y = 5x and r = 6x.

Q1) In questions 1 and 2, given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles :

(i) ∠3 and ∠6

(ii) ∠2 and ∠4

(iii) ∠3 and ∠7

(iv) ∠2 and ∠7

(v) ∠4 and∠6

(vi) ∠1 and ∠8

(vii) ∠1 and ∠5

(viii) ∠1 and ∠4

(ix) ∠5 and ∠7

Q2) (i) ∠1 and ∠4

(ii) ∠4 and ∠7

(iii) ∠10 and ∠12

(iv) ∠7 and ∠13

(v) ∠6 and ∠8

(vi) ∠11 and ∠8

(vii) ∠7 and ∠9

(viii) ∠4 and ∠5

(ix) ∠4 and ∠6

(x) ∠6 and ∠7

(xi) ∠2 and ∠13

Q3) In the given figures, the arrows indicate parallel lines. State which angles are equal. Give reasons.

Q4) In the given figure, find the measure of the unknown angles :

Q5) Which pair of the dotted line, segments, in the following figures, are parallel. Give reason:

Q6) In the given figures, the directed lines are parallel to each other. Find the unknown angles.

Q7) Find x y and p is the given figures:

Q8) Find x in the following cases :

Q1) Using ruler and compasses, construct the following angles :

(i)30°

(ii)15°

(iii) 75°

(iv) 180°

(v) 165°

(vi) 22.5°

(vii) 37.5°

(viii) 67.5°

Q2) Draw ∠ABC = 120°. Bisect the angle using ruler and compasses only. Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.

Q3) Draw a line segment PQ = 6 cm. Mark a point A in PQ so that AP = 2 cm. At point A, construct angle QAR = 60°.

Q4) Draw a line segment AB = 8 cm. Mark a point P in AB so that AP = 5 cm. At P, construct angle APQ = 30°.

Q5) Construct an angle of 75° and then bisect it.

Q6) Draw a line segment of length 6 .4 cm. Draw its perpendicular bisector.

Q7) Draw a line segment AB = 5.8 cm. Mark a point P in AB such that PB = 3.6 cm. At P, draw a perpendicular to AB.

Q8) In each case, given below, draw a line through point P and parallel to AB :