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Published on: 04/09/2019
Lines and Angles
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Questions + Answers key
Take MCQ Mathematics Test
1.
The angle which is equal to 8 times its compliment is:
\(80^{ 0 }\)
\(72^{ 0 }\)
\(90^{ 0 }\)
\(88^{ 0 }\)
2.
Which of the following is not a pair of supplementary angles?
\(90^{ 0 },90^{ 0 }\)
\(32^{ 0 },58^{ 0 }\)
\(0^{ 0 },180^{ 0 }\)
76,\(104^{ 0 }\)
3.
The angle of supplementary to \(90^{ 0 }\)+\(9^{ 0 }\) is
\(90^{ 0 }\)+\(9^{ 0 }\)
\(90^{ 0 }\)-\(9^{ 0 }\)
\(180^{ 0 }\)-âââââ+\(9^{ 0 }\)
\(180^{ 0 }\)-\(9^{ 0 }\)
4.
The compliment of (\(90^{ 0 }\)-\(a^{ 0 }\)) is
\(-a^{ 0 }\)
âââââ\(90^{ 0 }\)+\(a^{ 0 }\)
âââââ\(90^{ 0 }\)-\(a^{ 0 }\)
\(a^{ 0 }\)
5.
A straight angle
is greater than \(90^{ 0 }\) but less than \(180^{ 0 }\)
is exactly equal to \(90^{ 0 }\)
measures between \(0^{ 0 }\) and \(90^{ 0 }\)
is exactly equal to \(180^{ 0 }\)
6.
The sum of two complimentary angles is
\(180^{ 0 }\)
\(360^{ 0 }\)
\(90^{ 0 }\)
None of these
7.
How many types of angles are formed between the edges of plane surfaces?
Of different types
Of only one type
Of only two types
of only three types
8.
The minimum number of points required to draw a line is
1
2
3
4
9.
In figure, if y=\(20^{ 0 }\) , prove that the line AOB is a straight line.
10.
Ray OE bisects \(\angle \)AOB and OF the ray opposite to OE Show that \(\angle \)FOB=\(\angle \)FOA
11.
Let OA,AB, OC and OD by the rays in the anticlockwise direction starting from OA, such that \(\angle AOB=\angle COD=100^{ 0 };\angle AOD=\angle BOC=80^{ 0 }\) Is it true that AOC and BOD are straight lines? Justify your answer by drawing the figures.
12.
find the angles of a triangle PQR if \(\angle p-\angle q=45^{ 0 }\) and \(\angle Q-\angle R=30^{ 0 }\)
13.
In \(\triangle \) ABC if \(\angle A=(2Xx-5)^{ 0 },\angle B=(5X+5)^{ 0 }\) \(\angle C=(3Xx-50)^{ 0 }\) then find the values of x,\(\angle \) A ,\(\angle B\) and \(\angle C.\)
14.
In figure find the value of x.
15.
(a) In the figure , what value of x will make POQ a straight line:
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(b)In the given figure find the value of x,If AOB is a line
.png)
16.
In the given figure, what is the value of x?
17.
In the figure below, in \(\triangle ABC,\) AB=AC, then calculate the value of x.
18.
In the figure below, if \(\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=k\) right angles, then what is the value of k?
19.
In \(\triangle ABC,\angle A=\angle B/2=\angle C/6,\) then what will be the measurement of \(\angle A?\)
20.
In the figure below, if x,y and z are exterior angles of \(\triangle ABC\), then calculate the value of x+y+z.
21.
In the given figure, PQ||RS and EF||QS. If \(\angle PQS=60^o\), then what will be the measure of \(\angle RFE?\)
22.
If a transversal intersects two parallel lines, then which of the pairs of angles is equal.
23.
A transversal l intersects two lines m and n such that a pair of alternate interior angles is equal. Then, what can you say about the lines m and n?
24.
Write the complementary angle of 65o.
25.
What is the measure of an angle which is complement of itself?
1.
0=8\((90^{ 0 }-\theta )\)
2.
\(32^{ 0 }+,58^{ 0 }=90^{ 0 }\neq 180^{ 0 }\)
3.
Required angle=\(180^{ 0 }\)-(\(90^{ 0 }\)+\(9^{ 0 }\)) =\(90^{ 0 }\)+\(9^{ 0 }\)
4.
Complement of (\(90^{ 0 }\)-\(a^{ 0 }\))
=\(90^{ 0 }\)-(\(90^{ 0 }\)-\(a^{ 0 }\))=\(a^{ 0 }\)
5.
Definition of straight angle
6.
Definition of complementary angles
7.
(a)
Of different types
8.
(b)
2
9.
\(\because \) Sum of all the angle round a point is equal to \(360^{ 0 }\)
\(\therefore \) y+(3x-15)+(y+15)+2y+(4y+10)+x=\(360^{ 0 }\)
\(\Rightarrow \) 4x+8y=\(360^{ 0 }\)
\(\Rightarrow \) x+2y=\(90^{ 0 }\)
\(\Rightarrow \) x+2(\(20^{ 0 }\))=\(90^{ 0 }\)
\(\Rightarrow \) x+\(40^{ 0 }\)=\(90^{ 0 }\)
\(\Rightarrow x=50^{ 0 }\)
Now, y+3x-15+y+5=3x+2y-10
= 3(\(50^{ 0 }\))+2(\(20^{ 0 }\))-10
\(=150^{ 0 }+40^{ 0 }-10^{ 0 }\)
= \(180^{ 0 }\)
\(\therefore \) AOB is straight line.
10.
\(\angle \)FOB+\(\angle \)BOE=\(180^{ 0 }\) ...(1)
| Linear pair Axiom
\(\angle \)FOA+\(\angle \)AOE=\(180^{ 0 }\) .. (2)
| Linear Pair Axiom
From (1) and (2)
\(\angle \)FOB+\(\angle \)BOE=ââââââ\(\angle \) FOA+\(\angle \)AOE ....(3)
But \(\angle \)BOE=\(\angle \)AOE
\(\therefore \) From (3)
\(\Rightarrow \) \(\angle \)FOB=\(\angle \)FOA
11.
Yes ! AOC and BOD both are straight lines
12.
\(100^{ 0 },55^{ 0 },25^{ 0 }\)
13.
\(13;21^{ 0 },70^{ 0 },89^{ 0 }\)
14.
50
15.
(a) 28
(b) 26
16.
( )
Here, x+10o+x+x+20o=180o
3x=180o-30o=150o
\(x=\frac{150^o}{3}=50^o\)
17.
( )
AB=AC
\(\angle ACB=\angle B\)
In \(\triangle ABC, 80^o+\angle ACB+\angle B\)
=180o (Prop. of isosceles \(\triangle)\)
\(2\angle ACB=100^o\)
\(\angle ACB=50^o\)
Again, \(\angle ACB+x=180^o\) (Linear pair)
50o+x=180o
x=130o
18.
( )
In \(\triangle ABC,\)
\(\angle A+\angle B+\angle C=180^o\)
Also, in \(\triangle DEF,\)
\(\angle D+\angle E+\angle F=180^o\)
\(\therefore \angle A+\angle B+\angle C+\angle D+\angle E+\angle F=360^o\)
=4 X 90o
Hence,k=4 right angles.
19.
( )
In \(\triangle ABC,\)
\(\angle A+\angle B+\angle C=180^o\)(By given conditions)
\(\Rightarrow \angle A+2\angle A+6\angle A=180^o\)
\(\Rightarrow 9\angle A=180^o\)
\(\Rightarrow \angle A=20^o\)
20.
( )
Since sum of all the exterior angles formed by producing the sides of a polygon is 360o
xo+yo+zo=360o
21.
( )
\(\angle PQS+\angle QSF=180^o\) (Angles on the same side of transversal)
\(\Rightarrow\angle PQS+\angle RFE-180^o, as\ \angle QSF=\angle EFR\)
\(\Rightarrow 60^o+\angle RFE=180^o (Corresponding\ \angle S)\)
\(\therefore \angle RFE=120^o\)
22.
( )
Pair of alternate interior angles.
23.
( )
m and n lines are parallel.
24.
( )
Complementary angle of 65o
=90o-65o=25o (As sum of complementary angles is 90o )
25.
( )
Let the angle be x, then
Angle x= Complement of x
\(\Rightarrow\) x=90o-x\(\Rightarrow\)x=45o
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