R d sharma solutions mathematics class 7 Solutions for Chapter 14 lines and angles

Write down each pair of adjacent angles shown in fig. 13.

In Fig. 14, name all the pairs of adjacent angles.

In fig. 15, write down

(i) Each linear pair

(ii) Each pair of vertically opposite angles.

Are the angles 1 and 2 given in Fig. 16 adjacent angles?

Find the complement of each of the following angles:

(i) 35o

(ii) 72o

(iii) 45o

(iv) 85o

Find the supplement of each of the following angles:

(i) 70o

(ii) 120o

(iii) 135o

(iv) 90o

Identify the complementary and supplementary pairs of angles from the following pairs:

(i) 25o, 65o

(ii) 120o, 60o

(iii) 63o, 27o

(iv) 100o, 80o

Can two obtuse angles be supplementary, if both of them be

(i) Obtuse?

(ii) Right?

(iii) Acute?

Name the four pairs of supplementary angles shown in Fig.17.

In Fig. 18, A, B, C are collinear points and ∠DBA = ∠EBA.

(i) Name two linear pairs.

(ii) Name two pairs of supplementary angles.

If two supplementary angles have equal measure, what is the measure of each angle?

If the complement of an angle is 28o, then find the supplement of the angle.

In Fig. 19, name each linear pair and each pair of vertically opposite angles:

In Fig. 20, OE is the bisector of ∠BOD. If ∠1 = 70o, find the magnitude of ∠2, ∠3and ∠4.

One of the angles forming a linear pair is a right angle. What can you say aboutits other angle?

One of the angles forming a linear pair is an obtuse angle. What kind of angle is the other?

One of the angles forming a linear pair is an acute angle. What kind of angle is the other?

Can two acute angles form a linear pair?

If the supplement of an angle is 65o, then find its complement.

Find the value of x in each of the following figures.

In Fig. 22, it being given that ∠1 = 65o, find all other angles.

In Fig. 23, OA and OB are opposite rays:

(i) If x = 25o, what is the value of y?

(ii) If y = 35o, what is the value of x?

In Fig. 24, write all pairs of adjacent angles and all the liner pairs.

In Fig. 25, find ∠x. Further find ∠BOC, ∠COD and ∠AOD.

How many pairs of adjacent angles are formed when two lines intersect in a point?

How many pairs of adjacent angles, in all, can you name in Fig. 26?

In Fig. 27, determine the value of x

In Fig.28, AOC is a line, find x.

In Fig. 29, POS is a line, find x.

In Fig. 30, lines l1 and l2 intersect at O, forming angles as shown in the figure. If x= 45o , find the values of y, z and u.

In Fig. 31, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u

In Fig. 32, find the values of x, y and z.

In Fig. 58, line n is a transversal to line l and m. Identify the following:

(i) Alternate and corresponding angles in Fig. 58 (i)

(ii) Angles alternate to ∠d and ∠g and angles corresponding to ∠f and ∠h in Fig. 58 (ii)

(iii) Angle alternate to ∠PQR, angle corresponding to ∠RQF and angle alternate to ∠PQE in Fig. 58 (iii)

(iv) Pairs of interior and exterior angles on the same side of the transversal in Fig.58 (ii)

In Fig. 59, AB and CD are parallel lines intersected by a transversal PQ at L and M respectively, If ∠CMQ = 60o, find all other angles in the figure.

In Fig. 60, AB and CD are parallel lines intersected by a transversal by atransversal PQ at L and M respectively. If ∠LMD = 35o find ∠ALM and∠PLA.

The line n is transversal to line l and m in Fig. 61. Identify the angle alternate to∠13, angle corresponding to ∠15, and angle alternate to ∠15.

In Fig. 62, line l ∥ m and n is transversal. If ∠1 = 40°, find all the angles andcheck that all corresponding angles and alternate angles are equal.

In Fig.63, line l ∥ m and a transversal n cuts them P and Q respectively. If ∠1 =75°, find all other angles.

In Fig. 64, AB ∥ CD and a transversal PQ cuts at L and M respectively. If ∠QMD= 100o, find all the other angles

In Fig. 65, l ∥ m and p ∥ q. Find the values of x, y, z, t

In Fig. 66, line l ∥ m, ∠1 = 120o and ∠2 = 100o , find out ∠3 and∠4.

In Fig. 65, l ∥ m. Find the values of a, b, c, d. Give reasons.

In Fig. 68, AB ∥ CD and ∠1 and ∠2 are in the ratio of 3: 2. Determine all anglesfrom 1 to 8.

In Fig. 69, l, m and n are parallel lines intersected by transversal p at X, Y andZ respectively. Find ∠1, ∠2 and ∠3.

In Fig. 70, if l ∥ m ∥ n and ∠1 = 60o , find ∠2

In Fig. 71, if AB ∥ CD and CD ∥ EF, find ∠ACE

. In Fig. 72, if l ∥ m, n ∥ p and ∠1 = 85o , find ∠2.

In Fig. 73, a transversal n cuts two lines l and m. If ∠1 = 70o and ∠7 = 80o , is l ∥ m?

In Fig. 74, a transversal n cuts two lines l and m such that ∠2 = 65o and ∠8 =65o . Are the lines parallel?

In Fig. 75, Show that AB ∥ EF.

In Fig. 76, AB ∥ CD. Find the values of x, y, z.

In Fig. 77, find out ∠PXR, if PQ ∥ RS.

In Figure, we have

(i) ∠MLY = 2∠LMQ

(ii) ∠XLM = (2x – 10)o and ∠LMQ = (x + 30)o , find x.

(iii) ∠XLM = ∠PML, find ∠ALY

(iv) ∠ALY = (2x – 15)o , ∠LMQ = (x + 40)o , findx

In Fig. 79, DE ∥ BC. Find the values of x and y.

In Fig. 80, line AC ∥ line DE and ∠ABD = 32o , Find out the angles x and y if ∠E =122o .

In Fig. 81, side BC of ΔABC has been produced to D and CE ∥ BA. If ∠ABC =65o , ∠BAC = 55o , find ∠ACE, ∠ECD, ∠ACD.

In Fig. 82, line CA ⊥ AB ∥ line CR and line PR ∥ line BD. Find ∠x, ∠y,∠z.

In Fig. 83, PQ ∥ RS. Find the value of x.

In Fig. 84, AB ∥ CD and AE ∥ CF, ∠FCG = 90o and ∠BAC = 120o . Find the value of x, y and z.

In Fig. 86, state which lines are parallel and why?

In Fig. 87, the corresponding arms of ∠ABC and ∠DEF are parallel. If ∠ABC =75o , find ∠DEF.