1. State the property that is used in each of the following statements?
(i) If a ∥ b, then ∠1 = ∠5.
Solution:
The property of corresponding angles is used in the above statement.
(ii) If ∠4 = ∠6, then a ∥ b.
Solution:
The property of alternate interior angles is used in the above statement.
(iii) If ∠4 + ∠5 = 180o, then a ∥ b.
Solution:
The property of interior angles on the same side of the transversal is supplementary.
2. In the adjoining figure, identify:
(i) The pairs of corresponding angles.
Solution:
By observing the given figure, the pairs of corresponding angles are,
∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7
(ii) The pairs of alternate interior angles.
Solution:
By observing the given figure, the pairs of alternate interior angles are,
∠2 and ∠8, ∠3 and ∠5
(iii) The pairs of interior angles on the same side of the transversal.
Solution:
By observing the given figure, the pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8
(iv) The vertically opposite angles.
Solution:
By observing the given figure, the vertically opposite angles are,
∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8
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3. In the adjoining figure, p ∥ q. Find the unknown angles.
Solution:
By observing the given figure,
We know that, Linear pair is the sum of adjacent angles i.e 180o
Then,
∠e + 125o = 180o [Linear pair]
∠e = 180o – 125o
∠e = 55o
Now,
By the property of corresponding angles,
∠d = ∠125o
From the rule of vertically opposite angles,
∠f = ∠e = 55o
∠b = ∠d = 125o
By the property of corresponding angles,
∠c = ∠f = 55o
∠a = ∠e = 55o
4. Find the value of x in each of the following figures if l ∥ m.
(i)
Solution:
Let us assume that the other angle on the line m be ∠b,
Then,
By the property of corresponding angles,
∠b = 110o
We know that Linear pair is the sum of adjacent angles i.e 180o
Now,
∠x + ∠b = 180o
∠x + 110o = 180o
∠x = 180o – 110o
∠x = 70o
(ii)
Solution:
By the property of corresponding angles,
∠x = 100o
5. In the given figure, the arms of two angles are parallel.
If ∠ABC = 70o, then find
(i) ∠DGC
(ii) ∠DEF
(i) ∠DGC
Solution:
Given, lines A and D are parallel to each other.
Let us consider that AB ∥ DG
BC is the transversal line that intersects AB and DG
Now,
By the property of corresponding angles,
∠DGC = ∠ABC
Then,
∠DGC = 70o
(ii) ∠DEF
Solution:
Given, lines A and D are parallel to each other.
Let us consider that BC ∥ EF
DE is the transversal line that intersects BC and EF
Now,
By the property of corresponding angles,
∠DEF = ∠DGC
Then,
∠DEF = 70o
6. In the given figures below, decide whether l is parallel to m.
(i)
Solution:
Given, two lines l and m,
L ll m
n is the transversal line that intersects l and m.
We know that the sum of interior angles on the same side of transversal is 180o.
Then,
= 126o + 44o
= 170o
But, here the sum of interior angles on the same side of transversal is not equal to 180o.
Hence, line l is not parallel to line m.
(ii)
Solution:
Let us assume ∠a be the vertically opposite to the angle that formed due to the intersection of the straight line l and transversal n,
Then, ∠a = 75o
Let us consider the two lines l and m,
n is the transversal line intersecting l and m.
We know that the sum of interior angles on the same side of transversal is 180o.
Then,
= 75o + 75o
= 150o
But, the sum of interior angles on the same side of transversal is not equal to 180o.
Hence, line l is not parallel to line m.
(iii)
Solution:
Let us assume ∠a be the vertically opposite angle that formed due to the intersection of the Straight line l and transversal line n,
Let us consider the two lines l and m,
n is the transversal line intersecting l and m.
We know that the sum of interior angles on the same side of transversal is 180o.
Then,
= 123o + ∠a
= 123o + 57o
= 180o
We know that the sum of interior angles on the same side of transversal is equal to 180o.
Hence, line l is parallel to line m.
(iv)
Solution:
Let us assume ∠a be the angle that formed due to the intersection of the Straight line l and transversal line n,
We know that the Linear pair is the sum of adjacent angles is equal to 180o.
∠a + 98o = 180o
∠a = 180o – 98o
∠a = 82o
Now, we consider ∠a and 72o are the corresponding angles.
The corresponding angles should be equal to l and m to become parallel to each other.
But, in the given figure corresponding angles measures 82o and 72o respectively.
Hence, line l is not parallel to line m.
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Charges: Only ₹500/ month where you can ask your question face to face directly live. Each batch will have at max 100 students. Our main focus is to get full/full marks in your exam, in this way we will study there.
TUITION DURATION: – 1 hour: Monday to Saturday. Sunday- Off.
TIMING: – Before & After your school timing. We will discuss further on this topic.
FREE DEMO CLASS: 3
Seats are limited because of zoom classes. So, book your seat right now for free. Pay fee after demo classes directly on my upi id: maketoss@ybl
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