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Published on: 05/09/2019
Lines and Angle
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Questions + Answers key
Take MCQ Mathematics Test
1.
What will be the measure of the supplement of each one of the following angles? 55°
2.
Find the pairs of supplementary angles in the question figure.
3.
Find the pairs of supplementary angles in the question figure.
4.
Can two right angles be supplementary?
5.
Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.
6.
Find the measures of the angles made by the intersecting lines at the vertices of an equilateral triangle.
7.
Find the angle which is equal to its supplement.
8.
Find the angle, which is equal to its complement.
9.
In the given figure, the value of x is equal to 27.5
10.
An angle is more than 45°. Its complementary angle must be less than 45°.
11.
Two right angles are always supplementary to each other.
12.
Two supplementary angles are always obtuse angle.
13.
One obtuse and one acute angle can make a pair of complementary angles.
14.
Two right angles are complementary to each other.
15.
Iron rodes a, b, c, d, e and f are making a design of a bridge as shown in figure , in which a || b, c || d, e || f. Find the marked angles between d and f
16.
In the following figure, OB is perpendicular to OA and \(\angle\)BOC =49°. Find \(\angle\)AOD.
17.
The measure of an angle, which is four times its supplement is
36°
144°
16°
64°
18.
If two supplementary angles are in the ratio of 1 : 2, then the bigger angle is
120°
125°
110°
90°
19.
In the following figure, if AB II CD, \(\angle \)APQ = 50° and \(\angle \)PRD = 130°, then \(\angle \)QPR is
130°
50°
80°
30°
20.
Angles which are both supplementary and vertically opposite are
95°,85°
90°,90°
100°,80°
45°,45°
21.
The supplement of an acute is always _____________ angle.
22.
An angle which is half of its supplement is ______________
23.
An angle is 45°. Its complementary angle will be _____________
24.
Sum of interior angles on the same side of a transversal is ______________
25.
If sum of measures of two angles is 180°, then they are ___________________
26.
Lines l and m are parallel to each other, where line t is transversal line.
\(\angle \)4 is equal to
27.
Lines l and m are parallel to each other, where line t is transversal line.
\(\angle \)3 is equal to
28.
Lines l and m are parallel to each other, where line t is transversal line.
\(\angle \) 1 is equal to
29.
Complement of 42°
30.
Complement of 32°
1.
The supplement angle of 55° is 125°
2.
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.
3.
In this pair, measures of the given angles are 110° and 50°.
\(\therefore\) Sum of the given angles = 110° + 50° = 160°,
which is less than 180°.
So, this pair of angles is not supplementary.
4.
Yes, two right angles can be supplementary because the measure of each right angle is 90°, therefore the sum of two right angles would be 90° + 90° = 180°. So, the two right angles are supplementary.
5.
Let ABCD be the rectangle.
ABCD is a parallelogram with \(\angle \)A = 90°.
We have, \(\angle \)C = \(\angle \)A = 90°
[opposite angles of a parallelogram are equal]
Again, \(\angle \)A + \(\angle \)B= 180°
[\(\because\) \(\angle \)A and \(\angle \)B are adjacent angles of a parallelogram]
\(\Rightarrow\) 90° + \(\angle \)B= 180° \(\Rightarrow\) \(\angle \)B= 180° - 90° = 90°
\(\therefore\) \(\angle \)D = \(\angle \)B= 90°
[\(\because\) opposite angles of a parallelogram are equal]
Hence, \(\angle \)A = \(\angle \)B = \(\angle \)C = \(\angle \)D = 90°
6.
Let ABC be an equilateral triangle.
Since, all the angles of an equilateral triangle are equal.
\(\therefore\) \(\angle \)A = \(\angle \)B = \(\angle \)C = x° [say]
We know that, sum of all the angles of a triangle is 180°.
\(\therefore\) \(\angle \)A + \(\angle \)B + \(\angle \)C = 180°
\(\Rightarrow \) x° +x° +x° = 180°
\(\Rightarrow \) 3x° =180°
\(\Rightarrow \quad x°=\frac { 180° }{ 3 } =60°\)
Hence, \(\angle \)A = \(\angle \)B =\(\angle \)C= 60°
7.
Let the angle be x°,
Therefore, its supplement be 180°- x°,
Since, the angle is equal to its supplement.
\(\therefore\) x°=180°-x°
On transposing x° from RHS to LHS, we get
x°+ x°= 180° \(\Rightarrow\) 2x° = 180°
On dividing both sides by 2, we get
\(\therefore \quad { x }^{ ° }=\frac { 180° }{ 2 } =90°\)
Hence, the required angle is 90°.
8.
Let the angle be x°.
Therefore, its complement be 90° - x°,
Since, the angle is equal to its complement.
x°=90° - x°
On transposing from RHS to LHS, we get
x° + x° = 90° \(\Rightarrow\) 2x° = 90°
On dividing both sides by 2, we get
\(\frac { 2x }{ 2 } =\frac { 90° }{ 2 } \Rightarrow \quad x=45°\)
Hence, the required angle is 45°.
9.
(a)
10.
(a)
11.
(a)
12.
(b)
13.
(b)
14.
(b)
15.
Angle between d and f +
Angle between d and e = 180°
[\(\because\) pair of cointerior angles]
\(\therefore\) Angle between d and f = 180° - 105°= 75°
16.
Since, \(\angle\)AOB = 90° [right angle at O]
So, \(\angle\)AOB = \(\angle\)COB + \(\angle\)COA
\(\because\) \(\angle\)COB = 49° \(\Rightarrow\) \(\angle\)COA + 49° = 90° [given]
\(\Rightarrow\) \(\angle\)COA = 90° - 49° \(\Rightarrow\) \(\angle\)COA = 41°
Since, DC is a straight line, where \(\angle\)COA and \(\angle\)AOD form a linear pair .
So, \(\angle\)AOD + \(\angle\)COA =180°
\(\because\) \(\angle\)COA =41°
\(\therefore\) \(\angle\)AOD =180° - 41° \(\Rightarrow\) \(\angle\)AOD =139°
17.
(b)
144°
18.
(a)
120°
19.
(c)
80°
20.
(b)
90°,90°
21.
( )
obtuse
22.
( )
60°
23.
( )
45°
24.
( )
180°
25.
( )
supplementary
26.
( )
78°
27.
( )
102°
28.
( )
102°
29.
( )
48°
30.
( )
58°
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