Selina solutions concise mathematics class 6 icse Solutions for Chapter 25 properties of angles and lines including parallel lines

Exercises in Chapter 25 properties of angles and lines including parallel lines Grade 6

Exercise 25(A)

Exercise 25(B)

Exercise 25(C)

Exercise 25(D)

Revision Exercise

Questions in Exercise 25(A)

Q1)

Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find :

(i) angle BOD

(ii) ∠AOD

(iii) ∠BOC

Q2)

The adjoining figure, shows two straight lines AB and CD intersect at point P. If ∠BPC = 4x – 5° and ∠APD = 3x + 15° ; find :

(i) the value of x.

(ii) ∠APD

(iii) ∠BPD

(iv) ∠BPC

Q3)

The given diagram shows two adjacent angles AOB and AOC, whose exterior sides are along the same straight line. Find the value of x.

Q4)

Each figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line.

Q5)

A line segment AP stands at point P of a straight line BC such that ∠APB = 5x – 40° and ∠APC = .x+ 10°; find the value of x and angle APB.

Questions in Exercise 25(B)

Q1)

Identify the pair of angles in each of the figure given below :

adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.

(A) (i) $\angle2\ and\ \angle4$

(ii) $\angle1\ and\ \angle8$

(iii) $\angle4\ and\ \angle5$

(iv) $\angle1\ and\ \angle5$

(v) $\angle3\ and\ \angle5$

(B) (i) $\angle1\ and\ \angle10$

(ii) $\angle4\ and\ \angle8$

(iii) $\angle4\ and\ \angle8$

(iv) $\angle1\ and\ \angle5$

(v) $\angle4\ and\ \angle7$

(ii) $\angle6\ and\ \angle12$

(iii) $\angle8\ and\ \angle10$

(iv) $\angle4\ and\ \angle11$

(v) $\angle2\ and\ \angle8$

(vi) $\angle5\ and\ \angle7$

Q2)

Each figure given below shows a pair of parallel lines cut by a transversal For each case, find a and b, giving reasons.

Q3)

If ∠1 = 120°, find the measures of : ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8. Give reasons.

Q4)

In the figure given below, find the measure of the angles denoted by x,y, z,p,q and r.

Q5)

Using the given figure, fill in the blanks.

$\angle x=…………;\ \angle z=………..$

$\angle p=……….;\ \angle q=………$

$\angle r=……..;\ \angle s=………$

Q6)

In the given figure, find the angles shown by x,y, z and w. Give reasons.

Q7)

Find a, b, c and d in the figure given below :

Q8)

Find x, y and z in the figure given below :

Questions in Exercise 25(C)

Q1)

In your note-book copy the following angles using ruler and a pair compass only.

Q2)

Construct the following angles, using ruler and a pair of compass only

(i) 60°

(ii) 90°

(iii) 45°

(iv) 30°

(v) 120°

(vi) 135°

(vii) 15°

Q3)

Draw line AB = 6cm. Construct angle ABC = 60°. Then draw the bisector of angle ABC.

Q4)

Draw a line segment PQ = 8cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meet PQ at point R. Measure the lengths of PR and QR. Is PR = QR ?

Q5)

Draw a line segment AB = 7cm. Mark a point Point AB such that AP=3 cm. Draw perpendicular on to AB at point P.

Q6)

Draw a line segment AB = 6.5 cm. Locate a point P that is 5 cm from A and 4.6 cm from B. Through the point P, draw a perpendicular on to the line segment AB.

Questions in Exercise 25(D)

Q1)

Draw a line segment OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B; then measure the length of AB.

Q2)

Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.

Q3)

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

Q4)

Draw ∠PQR = 75° by using set- squares. On PQ mark a point M such that MQ = 3 cm. On QR mark a point N such that QN = 4 cm. Join M and N. Measure the length of MN.

Questions in Revision Exercise

Q1)

In the following figures, AB is parallel to CD; find the values of angles x, y and z :

Q2)

In each of the following figures, BA is parallel to CD. Find the angles a, b and c:

Q3)

In each of the following figures, PQ is parallel to RS. Find the angles a, b and c:

Q4)

Two straight lines are cut by a transversal. Are the corresponding angles always equal?

Q5)

Two straight lines are cut by a transversal so that the co-interior angles are supplementary. Are the straight lines parallel?

Q6)

Two straight lines are cut by a transversal so that the co-interior angles are equal. What must be the measure of each interior angle to make the straight lines parallel to each other ?

Q7)

In each case given below, find the value of x so that POQ is straight line

Q8)

in each case, given below, draw perpendicular to AB from an exterior point P

Q9)

Draw a line segment BC = 8 cm. Using set-squares, draw ∠CBA = 60° and ∠BCA = 75°. Measure the angle BAC. Also measure the lengths of AB and AC.

Q10)

Draw a line AB = 9 cm. Mark a point P in AB such that AP=5 cm. Through P draw (using set-square) perpendicular PQ = 3 cm. Measure BQ.

Q11)

Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.

Q12)

Without using set squares, construct angle ABC = 60° in which AB = BC = 5 cm. Join A and C and measure the length of AC.