Class 6 - Mathematics
Chapter - Lines and Angles : Exercise 5.2
Top Block 1
Question: 1.State the property that is used in each of the following statements:
- If a‖b, then ∠1 = ∠5.
- If ∠4 = ∠6, then a‖b.
- If ∠4 + ∠5 + 180o, then a‖b.
Answer :
(i) Given, a‖b then ∠1 = ∠5 [Corresponding angles]
If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.
(ii) Given, ∠4 = ∠6, then a‖b [Alternate interior angles]
When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines have to be parallel.
(iii) Given, ∠4 + ∠5 = 180o, then a‖b [pair of interior angles]
When a transversal cuts two lines, such that pairs of interior angles on the same side of transversal are supplementary, the lines have to be parallel.
Question: 2.In the adjoining figure, identify:
Mddle block 1
- the pairs of corresponding angles.
- the pairs of alternate interior angles.
- the pairs of interior angles on the same side of the transversal.
- the vertically opposite angles.
Answer :
(i) The pairs of corresponding angles:
∠1, ∠5; ∠2, ∠6; ∠4, ∠8 and ∠3, ∠7
(ii) The pairs of alternate interior angles are:
∠3, ∠5 and ∠2, ∠8
(iii) The pair of interior angles on the same side of the transversal:
∠3, ∠8 and ∠2, ∠5
(iv) The vertically opposite angles are:
∠1, ∠3; ∠2, ∠4; ∠6, ∠8 and ∠5, ∠7
Question: 3.In the adjoining figure, p‖q. Find the unknown angles.
Answer :
Given, p‖q and cut by a transversal line.
∵ 125o + e = 180o [Linear pair]
∴ e = 180o – 125o = 55o ……….(i)
Now e = f = 55o [Vertically opposite angles]
Also a = f = 55o [Alternate interior angles]
a + b = 180o [Linear pair]
⇒ 55o + b = 180o [From eq. (i)]
⇒ b = 180o – 55o = 125o
Now a = c = 55o and b = d = 125o [Vertically opposite angles]
Thus, a =55o, b = 125o, c = 55o, d = 125o, e = 55o and f = 55o.
Question: 4.Find the values of x in each of the following figures if l‖m.
Answer :
(i) Given, l‖m and t is transversal line.
∴ Interior vertically opposite angle between lines l and t = 110o.
∴ 110o + x = 180o [Supplementary angles]
⇒ x = 180o – 110o = 70o
(ii) Given, l‖m and t is transversal line.
x + 2x = 180 [Interior opposite angles]
⇒ 3x = 180o
⇒ x = 180o⁄3 = 60o
(iii) Given, l‖m and a‖b.
x = 100o [Corresponding angles]
Question: 5.In the given figure, the arms of two angles are parallel. If ΔABC = 70o, then find:
(ii) DEF
Answer :
(i) Given, AB ‖ DE and BC is a transversal line and ∠ABC = 70o
∵ ∠ABC = ∠DGC [Corresponding angles]
∴ ∠DGC = 70o ……….(i)
(ii) Given, BC ‖ EF and DE is a transversal line and ∠DGC = 70o
∵ ∠DGC = ∠DEF [Corresponding angles]
∴ ∠DEF = 70o [From eq. (i)]
Question: 6.In the given figures below, decide whether l is parallel to m.
Answer :
(i) 126o + 44o = 170o
l is not parallel to m because sum of interior opposite angles should be 180o.
(ii) 75o + 75o = 150o
l is not parallel to m because sum of angles does not obey the property of parallel lines.
(iii) 57o + 123o = 180o
l is parallel to m due to supplementary angles property of parallel lines.
(iv) 98o + 72o = 170o
l is not parallel to m because sum of angles does not obey the property of parallel lines.