Grade 9 : Mathematics - 5. Lines and Angles (Set 2)

Question 1

Two straight lines AB and CD intersect at a point $O$. If $\angle AOC = 48^\circ$, what is the measure of $\angle BOD$?

Accepted Answer

A) $48^\circ$

Answer

B) $132^\circ$

Answer

C) $42^\circ$

Answer

D) $90^\circ$

Question 2

An angle is equal to its complement. What is the measure of this angle?

Accepted Answer

B) $45^\circ$

Answer

A) $30^\circ$

Answer

C) $60^\circ$

Answer

D) $90^\circ$

Question 3

Two adjacent angles forming a linear pair on a straight line are in the ratio $4 : 5$. What is the measure of the smaller angle?

Accepted Answer

A) $80^\circ$

Answer

B) $100^\circ$

Answer

C) $40^\circ$

Answer

D) $90^\circ$

Question 4

If an angle is $30^\circ$ less than twice its supplement, what is the measure of the angle?

Accepted Answer

B) $110^\circ$

Answer

A) $70^\circ$

Answer

C) $120^\circ$

Answer

D) $100^\circ$

Question 5

Two parallel lines L1 and L2 are intersected by a transversal line T. Two interior angles on the same side of the transversal are labeled (2x + 10)° and (3x + 20)°.

Find the value of $x$.

Accepted Answer

B) 30

Answer

A) 25

Answer

C) 35

Answer

D) 40

Question 6

What is the measure of the reflex angle corresponding to an angle of $115^\circ$?

Accepted Answer

B) $245^\circ$

Answer

A) $65^\circ$

Answer

C) $180^\circ$

Answer

D) $205^\circ$

Question 7

If two parallel lines are intersected by a transversal, which of the following statements is always TRUE?

Accepted Answer

B) Corresponding angles are equal

Answer

A) Alternate interior angles are supplementary

Answer

C) Co-interior angles are equal

Answer

D) Vertically opposite angles are supplementary

Question 8

A ray OC stands on a line AB such that $\angle AOC = (3x + 15)^\circ$ and $\angle BOC = (2x - 10)^\circ$. Find the value of $x$.

Accepted Answer

A) 35

Answer

B) 30

Answer

C) 40

Answer

D) 25

Question 9

The measure of an angle which is 5 times its complement is:

Accepted Answer

B) $75^\circ$

Answer

A) $15^\circ$

Answer

C) $60^\circ$

Answer

D) $45^\circ$

Question 10

Lines AB and CD intersect at point $O$. If $\angle AOC + \angle BOD = 130^\circ$, what is the measure of $\angle AOC$?

Accepted Answer

A) $65^\circ$

Answer

B) $115^\circ$

Answer

C) $50^\circ$

Answer

D) $130^\circ$

Question 11

Line m is parallel to line n, intersected by transversal t. Angle 1 and Angle 8 are alternate exterior angles.

If Angle 1 measure is $72^\circ$, what is the measure of Angle 8?

Accepted Answer

B) $72^\circ$

Answer

A) $108^\circ$

Answer

C) $90^\circ$

Answer

D) $180^\circ$

Question 12

If the angle bisectors of two adjacent angles forming a linear pair intersect at a point, what is the angle between these two bisectors?

Accepted Answer

C) $90^\circ$

Answer

A) $45^\circ$

Answer

B) $60^\circ$

Answer

D) $180^\circ$

Question 13

Two complementary angles are in the ratio $2 : 3$. What is the measure of the larger angle?

Accepted Answer

B) $54^\circ$

Answer

A) $36^\circ$

Answer

C) $60^\circ$

Answer

D) $72^\circ$

Question 14

Line $PQ \parallel RS$ and a transversal intersects PQ at $X$ and RS at $Y$. If $\angle QXY = 65^\circ$, what is the measure of the consecutive interior angle $\angle XYS$?

Accepted Answer

B) $115^\circ$

Answer

A) $65^\circ$

Answer

C) $125^\circ$

Answer

D) $25^\circ$

Question 15

What is the measure of an angle whose supplement is 4 times its complement?

Accepted Answer

C) $60^\circ$

Answer

A) $30^\circ$

Answer

B) $45^\circ$

Answer

D) $75^\circ$

Question 16

Statement I: Vertically opposite angles formed by two intersecting lines are equal.

Statement II: The sum of two angles forming a linear pair is $180^\circ$.

Evaluate the truth of Statement I and Statement II.

Accepted Answer

A) Both Statement I and Statement II are true

Answer

B) Both Statement I and Statement II are false

Answer

C) Statement I is true but Statement II is false

Answer

D) Statement I is false but Statement II is true

Question 17

Line $AB \parallel CD$. A transversal EF intersects AB at $E$ and CD at $F$. If $\angle AEF = 55^\circ$ and $\angle EFD = x^\circ$ are alternate interior angles, what is the value of $x$?

Accepted Answer

B) 55

Answer

A) 125

Answer

C) 35

Answer

D) 90

Question 18

If an angle exceeds its supplement by $40^\circ$, what is the measure of the angle?

Accepted Answer

B) $110^\circ$

Answer

A) $70^\circ$

Answer

C) $140^\circ$

Answer

D) $100^\circ$

Question 19

Three distinct straight lines AB, CD, and EF intersect at a common single point O.

How many distinct pairs of vertically opposite angles are formed at point $O$?

Accepted Answer

C) 6

Answer

A) 3

Answer

B) 4

Answer

D) 8

Question 20

An angle is $18^\circ$ less than its complement. Find the measure of the angle.

Accepted Answer

A) $36^\circ$

Answer

B) $54^\circ$

Answer

C) $42^\circ$

Answer

D) $48^\circ$

Grade 9 : Mathematics - 5. Lines and Angles (Set 2)