Grade 9 : Mathematics - 5. Lines and Angles (Set 1)

Question 1

Two angles are complementary if the sum of their measures is equal to $90^\circ$.

If two angles are complementary and one angle measures $35^\circ$, what is the measure of the other angle?

Accepted Answer

A) $55^\circ$

Answer

B) $65^\circ$

Answer

C) $145^\circ$

Answer

D) $45^\circ$

Question 2

A linear pair consists of adjacent angles whose non-common arms form a straight line, summing to $180^\circ$.

If two angles form a linear pair and one angle is $110^\circ$, find the measure of the other angle.

Accepted Answer

B) $70^\circ$

Answer

A) $80^\circ$

Answer

C) $90^\circ$

Answer

D) $110^\circ$

Question 3

Lines AB and CD cross at point $O$, forming four distinct angles around $O$.

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

Accepted Answer

B) $48^\circ$

Answer

A) $132^\circ$

Answer

C) $42^\circ$

Answer

D) $90^\circ$

Question 4

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

Accepted Answer

C) $90^\circ$

Answer

A) $45^\circ$

Answer

B) $60^\circ$

Answer

D) $180^\circ$

Question 5

Parallel lines $l$ and $m$ are intersected by transversal $t$.

Line $l \parallel m$ and $t$ is a transversal. If an interior angle on one side of the transversal is $75^\circ$, what is the consecutive interior angle on the same side?

Accepted Answer

B) $105^\circ$

Answer

A) $75^\circ$

Answer

C) $15^\circ$

Answer

D) $115^\circ$

Question 6

An angle measures $x^\circ$. If its complement is $28^\circ$, find the value of $x$.

Accepted Answer

A) 62

Answer

B) 152

Answer

C) 52

Answer

D) 72

Question 7

If two parallel lines are cut by a transversal, then the alternate interior angles are always:

Accepted Answer

C) Equal

Answer

A) Complementary

Answer

B) Supplementary

Answer

D) Unequal

Question 8

In $ riangle ABC$, $\angle A = 50^\circ$ and $\angle B = 65^\circ$. What is the measure of $\angle C$?

Accepted Answer

A) $65^\circ$

Answer

B) $55^\circ$

Answer

C) $75^\circ$

Answer

D) $45^\circ$

Question 9

An exterior angle of a triangle is $120^\circ$, and one of its opposite interior angles is $50^\circ$. Find the measure of the other opposite interior angle.

Accepted Answer

B) $70^\circ$

Answer

A) $60^\circ$

Answer

C) $80^\circ$

Answer

D) $170^\circ$

Question 10

Two supplementary angles are in the ratio $4 : 5$. Find the measure of the smaller angle.

Accepted Answer

A) $80^\circ$

Answer

B) $100^\circ$

Answer

C) $40^\circ$

Answer

D) $90^\circ$

Question 11

If two adjacent angles on a straight line are $(2x + 10)^\circ$ and $(3x - 20)^\circ$, find the value of $x$.

Accepted Answer

A) 38

Answer

B) 36

Answer

C) 30

Answer

D) 40

Question 12

Line $l \parallel m$ cut by transversal $t$. Two corresponding angles are given as expressions of $x$.

If two corresponding angles formed by parallel lines cut by a transversal are $(3x + 15)^\circ$ and $(2x + 35)^\circ$, find the value of $x$.

Accepted Answer

B) 20

Answer

A) 15

Answer

C) 25

Answer

D) 30

Question 13

What is the measure of an angle which is four times its complement?

Accepted Answer

B) $72^\circ$

Answer

A) $18^\circ$

Answer

C) $36^\circ$

Answer

D) $144^\circ$

Question 14

Three angles $x^\circ$, $2x^\circ$, and $3x^\circ$ form a complete turn around a point.

If three angles around a single point are $x^\circ$, $2x^\circ$, and $3x^\circ$, find the value of $x$.

Accepted Answer

C) 60

Answer

A) 30

Answer

B) 45

Answer

D) 90

Question 15

In a right-angled triangle, if one angle is $90^\circ$, what is the sum of the remaining two acute angles?

Accepted Answer

B) $90^\circ$

Answer

A) $180^\circ$

Answer

C) $45^\circ$

Answer

D) $135^\circ$

Question 16

Four rays OA, OB, OC, OD radiate from point $O$.

Rays OA, OB, OC, and OD share origin $O$. If $\angle AOB = 80^\circ$, $\angle BOC = 100^\circ$, $\angle COD = 110^\circ$, and $\angle DOA = y^\circ$, find $y$.

Accepted Answer

A) 70

Answer

B) 80

Answer

C) 60

Answer

D) 50

Question 17

If two straight lines intersect each other, how many pairs of vertically opposite angles are formed?

Accepted Answer

B) 2 pairs

Answer

A) 1 pair

Answer

C) 3 pairs

Answer

D) 4 pairs

Question 18

$ riangle PQR$ with side QR extended to point $S$, creating exterior angle $\angle PRS$.

In $ riangle PQR$, side QR is produced to $S$. If exterior angle $\angle PRS = 130^\circ$ and interior angle $\angle Q = 60^\circ$, find $\angle P$.

Accepted Answer

A) $70^\circ$

Answer

B) $60^\circ$

Answer

C) $50^\circ$

Answer

D) $120^\circ$

Question 19

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

Accepted Answer

A) $110^\circ$

Answer

B) $70^\circ$

Answer

C) $140^\circ$

Answer

D) $100^\circ$

Question 20

Two parallel lines cut by a transversal forming consecutive interior angles $(x + 20)^\circ$ and $(2x + 10)^\circ$.

Interior angles on the same side of a transversal intersecting two parallel lines are $(x + 20)^\circ$ and $(2x + 10)^\circ$. Find $x$.

Accepted Answer

A) 50

Answer

B) 60

Answer

C) 40

Answer

D) 30

Grade 9 : Mathematics - 5. Lines and Angles (Set 1)