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QUESTION: 1

If two lines intersect at a point, then the vertically opposite angles are always ________

Solution:

If two lines intersect at a point, then the vertically opposite angles are always equal

QUESTION: 2

Two angles forming a linear pair are ________________.

Solution:

Two angles forming a linear pair are supplementary

QUESTION: 3

A line that intersects two or more lines at distinct points is called

Solution:

A line that intersects two or more lines at distinct points is called transversal

QUESTION: 4

If two adjacent angles are supplementary, then they form _________ .

Solution:

A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then they are supplementary.

QUESTION: 5

If two angles are supplementary then the sum of their measures is __________.

Solution:

If two angles are supplementary then the sum of their measures is 180^{°}

QUESTION: 6

If two angles are complementary, then the sum of their measures is __________.

Solution:

If two angles are complementary, then the sum of their measures is 90^{°}.

QUESTION: 7

If ∠S and 100° form a linear pair. What is the measure of ∠S

Solution:

∠S and 100° form a linear pair i.e,

∠S + 100° = 180°

∠S = 180deg - 100°

∠S = 80°

QUESTION: 8

In figure pair of alternate interior angles are :

Solution:

**Alternate interior angles** are formed when a transversal passes through two lines. The **angles** that are formed on opposite sides of the transversal and inside the two lines are **alternate interior angles**. The theorem says that when the lines are parallel, that the **alternate interior angles** are equal.

So in the given figure ∠2, ∠3 are alternate interior angles

QUESTION: 9

Find the measure of an angle, if 7 times its complement is 10 less than 3 times its supplement

Solution:

Let the angle be x

measure of its complement = (90-x)

measure of its supplement= (180-x)

7(90-x) =3(180-x)-10

630 - 7x=540x-3x -10

-7x+3x= 530-630

-4x=-100

x= 100/4

x=25

QUESTION: 10

Find the measure of angle which is 32 less than its supplement

Solution:

Let the supplement angle be x

given:

(x-32) + x = 180

2x = 212

x= 106

The angles are 106 and 74

QUESTION: 11

The angle which makes a linear pair with an angle of 61deg is of

Solution:

Linear pair has a sum of 180 degrees

So x+61 =180

x=180 - 61 =119 degrees

QUESTION: 12

The sum of all angles around a point is

Solution:

The sum of all angles around a point is 360deg

QUESTION: 13

If two lines are intersected by a transversal such that any pair of corresponding angles are equal then the lines are

Solution:

If two lines are intersected by a transversal such that any pair of corresponding angles are equal then the lines are parallel

QUESTION: 14

Solution:

Its a straight angle which is equal to 180 degrees.

So ,6y+y+2y = 180

9y = 180

y= 180/9 = 20 degrees

QUESTION: 15

A and B are vertically opposite angles. If the measure of A is 60^{o}, what is the value of B?

Solution:

When two lines intersect, then vertically opposite angles so formed are equal

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