The minimum number of points required to draw a line is 

1

(a)

1

(b)

2

(c)

3

(d)

4

How many types of angles are formed between the edges of plane surfaces? 

1

(a)

Of different types

(b)

Of only one type

(c)

Of only two types

(d)

of only three types 

Two angles whose sum is \(90^{ 0 }\) are called

1

(a)

supplementary angles

(b)

complementary angles 

(c)

corresponding angles

(d)

alternate angles

The sum of two complimentary angles is 

1

(a)

\(180^{ 0 }\)

(b)

\(360^{ 0 }\)

(c)

\(90^{ 0 }\)

(d)

None of these

An angle which is greater than \(90^{ 0 }\) and less than \(180^{ 0 }\) is called 

1

(a)

an acute angle

(b)

a straight angle

(c)

an obtuse angle

(d)

an straight angle

A straight angle

1

(a)

is greater than \(90^{ 0 }\) but less than \(180^{ 0 }\)

(b)

is exactly equal to \(90^{ 0 }\)

(c)

measures between \(0^{ 0 }\) and \(90^{ 0 }\)

(d)

is exactly equal to \(180^{ 0 }\)

The compliment of (\(90^{ 0 }\)-\(a^{ 0 }\)) is

1

(a)

\(-a^{ 0 }\)

(b)

​​​​​\(90^{ 0 }\)+\(a^{ 0 }\)

(c)

​​​​​\(90^{ 0 }\)-\(a^{ 0 }\)

(d)

\(a^{ 0 }\)

The angle of supplementary to \(90^{ 0 }\)+\(9^{ 0 }\) is

1

(a)

\(90^{ 0 }\)+\(9^{ 0 }\)

(b)

\(90^{ 0 }\)-\(9^{ 0 }\)

(c)

\(180^{ 0 }\)-​​​​​+\(9^{ 0 }\)

(d)

\(180^{ 0 }\)-\(9^{ 0 }\)

Which of the following is not a pair of supplementary angles?

1

(a)

\(90^{ 0 },90^{ 0 }\)

(b)

\(32^{ 0 },58^{ 0 }\)

(c)

\(0^{ 0 },180^{ 0 }\)

(d)

76,\(104^{ 0 }\)

The angle which is equal to 8 times its compliment is:

1

(a)

\(80^{ 0 }\)

(b)

\(72^{ 0 }\)

(c)

\(90^{ 0 }\)

(d)

\(88^{ 0 }\)

What is the measure of an angle which is complement of itself?

1

(a)

Let the angle be x, then
Angle x= Complement of x
\(\Rightarrow\) x=90^o-x\(\Rightarrow\)x=45^o

Write the complementary angle of 65^o.

1

(a)

Complementary angle of 65^o
=90^o-65^o=25^o (As sum of complementary angles is 90^o )

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?

1

(a)

m and n lines are parallel.

If a transversal intersects two parallel lines, then which of the pairs of angles is equal.

1

(a)

Pair of alternate interior angles.

In the given figure, PQ||RS and EF||QS. If \(\angle PQS=60^o\), then what will be the measure of \(\angle RFE?\)

1

(a)

\(\angle PQS+\angle QSF=180^o\) (Angles on the same side of transversal)
\(\Rightarrow\angle PQS+\angle RFE-180^o, as\ \angle QSF=\angle EFR\)
\(\Rightarrow 60^o+\angle RFE=180^o (Corresponding\ \angle S)\)
\(\therefore \angle RFE=120^o\)

In the figure below, if x,y and z are exterior angles of \(\triangle ABC\), then calculate the value of x+y+z.

1

(a)

Since sum of all the exterior angles formed by producing the sides of a polygon is 360^o
x^o+y^o+z^o=360^o

In \(\triangle ABC,\angle A=\angle B/2=\angle C/6,\) then what will be the measurement of \(\angle A?\)

1

(a)

In \(\triangle ABC,\)
\(\angle A+\angle B+\angle C=180^o\)(By given conditions)
\(\Rightarrow \angle A+2\angle A+6\angle A=180^o\)
\(\Rightarrow 9\angle A=180^o\)
\(\Rightarrow \angle A=20^o\)

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?

1

(a)

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 90^o
Hence,k=4 right angles.

In the figure below, in \(\triangle ABC,\) AB=AC, then calculate the value of x.

1

(a)

AB=AC
\(\angle ACB=\angle B\)
In \(\triangle ABC, 80^o+\angle ACB+\angle B\)
=180^o (Prop. of isosceles \(\triangle)\)
\(2\angle ACB=100^o\)
\(\angle ACB=50^o\)
Again, \(\angle ACB+x=180^o\) (Linear pair)
50^o+x=180^o
x=130^o

In the given figure, what is the value of x?

1

(a)

Here,  x+10^o+x+x+20^o=180^o
3x=180^o-30^o=150^o
\(x=\frac{150^o}{3}=50^o\)

(a) In the figure , what value of x will make POQ a straight line:

(b)In the given figure find the value of x,If AOB is a line

2

(a)

In figure find the value of x.

2

(a)

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 \(\angle C.\)

2

(a)

find the angles of a triangle PQR if \(\angle p-\angle q=45^{ 0 }\) and \(\angle Q-\angle R=30^{ 0 }\)

2

(a)

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.

2

(a)

In figure If x+y=w+z then prove that AOB is a line

3

(a)

Ray OE bisects \(\angle \)AOB and OF the ray opposite to OE Show that \(\angle \)FOB=\(\angle \)FOA

4

(a)

In figure, if y=\(20^{ 0 }\) , prove that the line AOB is a straight line.

4

(a)