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Published on: 05/03/2019
Lines and Angle Important Questions
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Questions + Answers key
Take MCQ Mathematics Test
1.
CD intersects the line AB at F,\(\angle CFB=50^0\) and \(\angle EFA=\angle AFD.\)Find the measure of \(\angle EFC.\)
2.
Find an angle whose supplement is \(\frac { 2 }{ 3 } \) of its complement.
3.
In the figures given below, decide whether I is parallel to m
4.
Name the pairs of angles in each figure.
5.
In the adjoining figure, name the following pairs of angles.
Equal supplementary angles.
6.
An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?
7.
In the adjoining figure, which of the following are adjacent angles?
\(\angle \) BOD and \(\angle \)BOC
Justify your answer.
8.
Find the pairs of supplementary angles in the question figure.
9.
Which pairs of the following angles are complementary?
10.
What is the measure of the complement of each of the following angles? 65°
11.
Two angles forming a linear pair are _______________
12.
Find the value of x in each of the following figures, if 1|| m.
13.
In the adjoining figure, show that CD || EF.
14.
15.
In the following figure, PQ II RT. Find the value of a + b.
16.
In the following figure, find the value of x, if the lines I and m are parallel lines and line t is a transversal to line 1 and m
17.
In the given figure, PQ, RS, and UT are parallel lines.
(a) If c = 570 and \(a=\frac{c}{3}\) then find the value of d.
(b) If c = 75° and \(a=\frac{2}{3}c\) then find the value of b.
18.
In the given figure, PQ II RS. If 1 = (2a + b)0 and \(\angle 6=(3a-b)^0\) then find the measure of \(\angle 2\) in terms of b.
19.
In the given figure, AB II CO. Find the value of (i) w
(ii) x
(iii) y
20.
In the given figure, examine whether the following pairs of lines are parallel or not.
EF and GH
21.
Lines l||m, p||q, Find a, b, c, d?
22.
In the following figure, if \(\angle 1+\angle 2=100^\circ\) , then the measure of \(\angle 4\) is equal to
50°
100°
80°
130°
23.
In the following figure, a transversal cuts two parallel lines land m at points G and H respectively and the angles thus formed are marked. If \(\angle 1\) is an acute angle, then, which of the following statements is false?
\(\angle 1+\angle 2=180^\circ\)
\(\angle 2+\angle 5=180^\circ\)
\(\angle 3+\angle 8=180^\circ \)
\(\angle 2+\angle 6=180^\circ\)
24.
In the following figure, two straight lines AB and CD are intersecting each other at the point O and the angles thus formed at O are marked, then the value of \(\angle x-\angle y\) is
56°
118°
62°
180°
25.
The sum of the measures of the angles in a linear pair is
90°
180°
360°
none of these
26.
The measure of the supplement of the angle 90° is
45°
60°
30°
90°
27.
The measure of the complement of the angle 45° is
90°
45°
15°
135°
28.
If two lines are perpendicular to the same line. then they are:
perpendicular to each other
parallel to each other
either parallel to each other or perpendicular to each other
intersecting lines.
29.
In Fig., line l intersects two parallel lines PQ and RS. Then, which one of the following is not true?
\(\angle 1=\angle 3\)
\(\angle 2=\angle 4\)
\(\angle 6=\angle 7\)
\(\angle 4=\angle 8\)
30.
In which of the following figures, a and bare forming a pair of adjacent angles?
31.
Statements a and b are as given below:
a: If two lines intersect, then the vertically opposite angles are equal.
b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°.
Then
Both a and b are true
a is true and b is false
a is false and b is true
both a and b are false
32.
PA II BC II DT II and AB II DC. Then, the values of a and b are respectively.
60° ,30°
50° , 130°
70° , 1100
80° ,100°
33.
If angle P and angel Q are supplementary and the measure of angles p is 60°, then the measure of angle Q is:
120°
60°
30°
20°
34.
PQ is a mirror, AB is the incident ray and BC is the reflected ray. If \(\angle ABC=46^0\) then \(\angle ABP\) is equal to:
44°
67°
13°
62°
35.
Which of the following pair of angles are supplementary?
48° ,42°
60°,60°
75°, 105
179°,2°
36.
In the given figure, PQ II RS. If \(\angle\)1 = (2a + b)° and \(\angle\)6 = (3a - b)°, then the measure of \(\angle\)2 in terms of b is
(2+b)°
(3-b)°
(108-b)°
(180-b)°
37.
In the given figure, if PA II BC IIDT and AB II DC, then the values of a and b are respectively
60° and 120°
50° and 130°
70° and 110°
80° and 100°
38.
In the following figure, the value of \(\alpha\) is
20°
15°
25°
30°
39.
The angle, which makes a linear pair with an angle of 58° is of
122°
123°
119°
69°
40.
One obtuse angle and one acute angle can make a pair of supplementary angles.
1.
Let \(\angle EFC=x\)
Then \(\angle AFD=x\)
It is given that CD intersects line AB at F.
Therefore,\(\angle CFB=\angle AFD\) (vertically opposite angles)
So,x=500
But \(\angle EFA=\angle AFD\) which gives \(\angle EFA=50^0\)
Now, \(\angle CFB+\angle EFA+\angle EFC=180^0\) [as AB is a straight line]
\(50^0+50^0+\angle EFC=180^0\)
\(\angle EFC=180^0-100^0\)
Thus,\(\angle EFC=80^0\)
2.
Let x be the complement of an angle, then the angle will be \(\frac { 2 }{ 3 } \)x.
We know that, sum of complementary angle is 90°
So, \(x+\frac { 2 }{ 3 } x=90°\quad \Rightarrow \frac { 3x+2x }{ 3 } =90°\)
\(\Rightarrow \quad 5\times =270°\quad \Rightarrow x=\frac { 270° }{ 5 } =54°\Rightarrow x=54°\)
\(\therefore \quad \frac { 2 }{ 3 } \times { 54 }^{ ° }=2\times 18°=36°\)
Hence, complement angle of 54° is 36°
3.
Since, n is a transversal to l and m.
\(\therefore\) \(\angle \)1 = 75°
[ vertically opposite angles]
Also, \(\angle \)1 = 75° = 75° + 75° = 150°
\(\therefore\) 150° \(\neq \) 180°
So, l and m are not parallel.
4.
\(\angle \)3 and \(\angle \)4 are alternate interior angles
5.
Equal supplementary angles are \(\angle \)BOE and \(\angle \)EOD
6.
We know that, the sum of two complementary angles is 90°. So, if an angle is greater than 45°, then its complementary angle would be less than 45°.
7.
\(\angle \)BOD and \(\angle \)BOC are not adjacent angles because their other arms OD and OC are not on the opposite of the common arm OB, as shown in adjoining figure.
8.
In this pair, measures of the given angles are 50° and 130°.
\(\therefore\) Sum of the given angles = 50° + 130° = 180°,
So, this pair of angles is supplementary.
9.
In this pair, sum of two angles = 70° + 20° = 90° So, this pair of angles is complementary.
10.
Let the complement angle of 65° be x°.
We know that, the sum of two complementary angles is 90°.
\(\therefore\) x° + 65° = 90° \(\Rightarrow\) x°= 90° - 65° = 25°
[transposing 65° to RHS]
Hence, the complement angle of 65° is 25°.
11.
( )
adjacent angles or supplementary.
12.
x + 2x = 180° (Co-interior angle)
3x = 180°
x = 60°
13.
∵ \(\angle \) BAD = \(\angle \)BAE + \(\angle \)EAD
= 40° + 30° = 70°
and \(\angle \)CDA = 7·0°
∴\(\angle \)BAD = \(\angle \)CDA
But they form a pair of alternate angles.
=> AB || CD ...(1)
Also, \(\angle \)BAE + \(\angle \)AEF = 40° + 140° = 180°
But they form a pair of interior opposite angles.
=>AB || EF
From (1) and (2), we get
AB || CD || EF
=> CD || EF
14.
a + 60° = 180°
\(\Rightarrow \) a = 180° - 60° = 120°
a = d = 120° [alternate exterior angles]
b + d = 180° [linear pair]
\(\Rightarrow \) b + 120° = 180°
\(\Rightarrow \) b = 180° - 120° = 60°
\(\Rightarrow \) c = b = 60°. [vertically opp. angles.]
15.
Since, PQ||RT and RQ is a transversal line.
\(\angle \)RPQ and \(\angle \)a are corresponding angles.
\(\therefore \quad \angle RPQ=\angle a\Rightarrow \angle a=45°\)
Also, \(\angle \)b and \(\angle \) RQP are alternate angles.
\(\therefore\) \(\angle \)b= 55°
Hence, \(\angle \)a + \(\angle \) b = 45° + 55° =100°
16.
Since, lines I and m are parallel to each other, where line t is intersecting both these lines at the point 0 and M, respectively.
So, \(\angle \)OMA and \(\angle \)BME are vertically opposite angles.
So, \(\angle \)OMA = 42°
Also, \(\angle \)OMA and \(\angle \)x are interior angles.
So, \(\angle \)x + \(\angle \)OMA =180° \(\Rightarrow\) \(\angle \)x = 180° - 42° = 138°
17.
Given, PQ II RS II UT
(a) Given, c = 57° and \(a=\frac{c}{3}\)
\(\because PQ||UT\)
\(\therefore \angle UTP=\angle QPT\) [alternate interior angles]
\(\Rightarrow \angle c=\angle a+\angle b[\because QPT=a+b]\)
\(\Rightarrow 57^0=\frac{57^0}{3}+\angle b\)
\(\Rightarrow 57^0-19^0=\angle b\)
\(\Rightarrow \angle b=38^0\)
\(\therefore \angle b+\angle d=180^0\)
\(\Rightarrow \angle d=180^0-38^0=142^0\)
(b) Given, c = 75° and \(a=\frac{2}{3}c\)
\(\Rightarrow c=75^0\) and \(a=\frac{2}{5}\times75^0=30^0\)
\(\therefore \angle c=\angle a+\angle b\) [alternate interior angles]
\(\Rightarrow 75^0=30^0+\angle b\)
\(\Rightarrow 75^0-30^0=\angle b\)
\(\Rightarrow \angle b=45^0\)
18.
Given,\(\angle 1=(2a+b)^0\) and \(\angle 6=(3a-b)^0\)
so, \(\angle 1=\angle 7\) [alternate exterior angles]
So, we have \(\angle 7=(2a+b)^0\)
\(\therefore \angle 6+\angle 7=180^0\) [linear pair]
\(\Rightarrow\) (3a-b)0 + (2a + b)0 = 180°
\(\Rightarrow\) 3a- b + 2a + b = 180°
\(\Rightarrow\) 5a = 180°
on dividing both sides by 5, we get
\(\Rightarrow a=\frac{180^0}{5}=36^0\)
\(\because \angle 1+\angle 2=180^0\) [linear pair]
\(\Rightarrow 2a+b+\angle 2=180^0\)
\(\Rightarrow 2\times36^0+b+\angle 2=180^0\)
\( \Rightarrow b+\angle 2=180^0-72^0\)
\(\Rightarrow b+\angle 2=180^0\)
\(\therefore \angle 2=(108-b)\)
19.
75, 75, 60
20.
Given, \(\angle \)PSR = 115°; \(\angle \)RQD = 70° and \(\angle \)CPF = 65°
\(\angle \) PQR + \(\angle \)RQD = 180° [linear pair]
\(\Rightarrow\) \(\angle \)PQR = 180° - 70° \(\Rightarrow\) \(\angle \)PQR = 110°
\(\angle \)CPF = \(\angle \)SPQ = 65 °
[vertically opposite angles]
If EF || GH
Then, according to the definition of cointerior angles, the sum of \(\angle \)SPQ + \(\angle \)RQP should be 180°.
\(\therefore\) 65° + 110° = 175° \(\neq \) 180 °
So, EF is not parallel to GH.
21.
Given, p || q and I is a transversal.
We know that, the sum of pair of interior angles on the same sides of the transversal is supplementary.
\(\therefore\) \(\angle \)a + 60° = 180° \(\Rightarrow\) \(\angle \)a = \(\angle \)180° - 60° = 120°
and I || m and q is a transversal.
\(\therefore\) \(\angle \)a = \(\angle \)1 [pair of corresponding angles]
\(\angle \)1 = 120°
and \(\angle \)d= \(\angle \)1= 120° [vertically opposite angles]
Now, \(\angle \)1 + \(\angle \)c= 180°
[\(\because\) sum of the angles on the same side of a transversal is 180°]
\(\Rightarrow\) 120° + \(\angle \)c = 180° \(\Rightarrow\) \(\angle \)c = 180° -120° = 60°
\(\Rightarrow\) \(\angle \)b = \(\angle \)c = 60° [vertically opposite angles]
Hence, \(\angle \)a = 120°, \(\angle \)b = 60°, \(\angle \)c = 60° and \(\angle \)d=120°
22.
\(\angle 1=\angle 2;\angle 2+\angle 2=100^\circ\)
\(\therefore \angle 1=50^\circ\)
\(\therefore \angle 4\) = 180° - 50° = 130°.
23.
\(\angle 2=\angle 6\), corresponding angles.
24.
\(\angle x-\angle y\) = (180° - 62°) - 62°
= 118° - 62° = 56°.
25.
Definition of a linear pair of angles.
26.
180° - 90° = 90°.
27.
90° - 45° = 45°.
28.
(b)
parallel to each other
29.
(d)
\(\angle 4=\angle 8\)
30.
(d)
31.
(b)
a is true and b is false
32.
(b)
50° , 130°
33.
(a)
120°
34.
(b)
67°
35.
(c)
75°, 105
36.
(c)
(108-b)°
37.
(b)
50° and 130°
38.
(b)
15°
39.
(a)
122°
40.
(a)
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