Grade 9 : Mathematics - 5. Lines and Angles (Set 3)

Question 1

Two adjacent angles on a straight line AB form a linear pair.

If the measures of the two adjacent angles are $(3x - 10)^\circ$ and $(2x + 15)^\circ$, find the value of $x$ and the measure of the larger angle.

Accepted Answer

A) $x = 35$, larger angle = $95^\circ$

Answer

B) $x = 33$, larger angle = $89^\circ$

Answer

C) $x = 35$, larger angle = $85^\circ$

Answer

D) $x = 40$, larger angle = $110^\circ$

Question 2

An angle measure is defined relative to its complement and supplement.

An angle is $24^\circ$ more than its complement. What is the measure of the supplement of this angle?

Accepted Answer

B) $123^\circ$

Answer

A) $57^\circ$

Answer

C) $147^\circ$

Answer

D) $114^\circ$

Question 3

Lines $AB \parallel CD$. Transversal EF intersects AB at $P$ and CD at $Q$.

If the bisectors of co-interior angles $\angle BPQ$ and $\angle DQP$ intersect at point $R$, what is the measure of $\angle PRQ$?

Accepted Answer

C) $90^\circ$

Answer

A) $60^\circ$

Answer

B) $75^\circ$

Answer

D) $120^\circ$

Question 4

Line AB is parallel to line CD. Point $E$ lies between the two parallel lines.

Given $\angle ABE = 40^\circ$ and $\angle CDE = 30^\circ$, find the measure of the reflex angle $\angle BED$.

Accepted Answer

A) $290^\circ$

Answer

B) $250^\circ$

Answer

C) $310^\circ$

Answer

D) $70^\circ$

Question 5

On a straight line AOB, two rays OC and OD stand such that $C$ and $D$ lie on the same side of AB.

If $\angle AOC : \angle COD : \angle DOB = 2 : 3 : 4, find the measure of\angle COD$.

Accepted Answer

B) $60^\circ$

Answer

A) $40^\circ$

Answer

C) $80^\circ$

Answer

D) $100^\circ$

Question 6

In $ riangle ABC$, side BC is extended to point $D$. Ray CE is drawn parallel to side AB.

If $\angle A = 55^\circ$ and $\angle B = 65^\circ$, find the measure of $\angle ECD$.

Accepted Answer

C) $65^\circ$

Answer

A) $55^\circ$

Answer

B) $60^\circ$

Answer

D) $120^\circ$

Question 7

Two straight lines AB and CD intersect at point $O$.

If $\angle AOC + \angle BOD = 130^\circ$, find the measures of $\angle AOC$ and $\angle AOD$.

Accepted Answer

A) $\angle AOC = 65^\circ, \angle AOD = 115^\circ$

Answer

B) $\angle AOC = 50^\circ, \angle AOD = 130^\circ$

Answer

C) $\angle AOC = 65^\circ, \angle AOD = 125^\circ$

Answer

D) $\angle AOC = 75^\circ, \angle AOD = 105^\circ$

Question 8

In $ riangle PQR$, side QR is produced to $S$. The bisector of $\angle PQR$ and the bisector of exterior angle $\angle PRS$ meet at point $T$.

If $\angle QPR = 70^\circ$, what is the measure of $\angle QTR$?

Accepted Answer

A) $35^\circ$

Answer

B) $45^\circ$

Answer

C) $50^\circ$

Answer

D) $70^\circ$

Question 9

An angle $x$ has the property that its measure is equal to $\frac{2}{3}$ of its supplement.

Find the measure of the complement of angle $x$.

Accepted Answer

C) $18^\circ$

Answer

A) $72^\circ$

Answer

B) $108^\circ$

Answer

D) $28^\circ$

Question 10

Parallel lines AB and CD are intersected by a transversal $t$.

Two interior angles on the same side of $t$ are $(4x + 15)^\circ$ and $(3x + 25)^\circ$. Find $x$ and the measure of the smaller angle.

Accepted Answer

A) $x = 20$, smaller angle = $85^\circ$

Answer

B) $x = 20$, smaller angle = $95^\circ$

Answer

C) $x = 18$, smaller angle = $79^\circ$

Answer

D) $x = 22$, smaller angle = $91^\circ$

Question 11

Line $AB \parallel CD$. A point $E$ is located between the two parallel lines such that segments BE and DE are connected.

If reflex angle $\angle ABE = 120^\circ$ (interior co-angle) and interior angle $\angle CDE = 140^\circ$, find interior angle $\angle BED$.

Accepted Answer

B) $100^\circ$

Answer

A) $80^\circ$

Answer

C) $120^\circ$

Answer

D) $260^\circ$

Question 12

In $ riangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$.

If $\angle BOC = 125^\circ$, find the measure of angle $\angle A$.

Accepted Answer

C) $70^\circ$

Answer

A) $55^\circ$

Answer

B) $60^\circ$

Answer

D) $80^\circ$

Question 13

Line PQ is perpendicular to line RS at point $O$. Ray OT is drawn lying between OP and OR.

If $\angle ROT = 38^\circ$, find the measure of $\angle POT$ and its reflex angle.

Accepted Answer

A) $\angle POT = 52^\circ$, reflex = $308^\circ$

Answer

B) $\angle POT = 38^\circ$, reflex = $322^\circ$

Answer

C) $\angle POT = 52^\circ$, reflex = $232^\circ$

Answer

D) $\angle POT = 142^\circ$, reflex = $218^\circ$

Question 14

Consider the following two statements regarding parallel lines cut by a transversal:
Statement I: The bisectors of any pair of alternate interior angles are parallel to each other.
Statement II: The bisectors of any pair of consecutive interior angles on the same side of transversal intersect at right angles.

Which of the above statements is/are correct?

Accepted Answer

C) Both Statement I and Statement II

Answer

A) Statement I only

Answer

B) Statement II only

Answer

D) Neither Statement I nor Statement II

Question 15

Three parallel lines $AB \parallel CD \parallel EF$ are intersected by a transversal GH. The ratio of co-interior angle $y$ to alternate interior angle $z$ is $y : z = 3 : 7$.

Find the value of $x$, where $x$ and $y$ are co-interior angles on the same side of the transversal between AB and CD.

Accepted Answer

A) $126^\circ$

Answer

B) $54^\circ$

Answer

C) $108^\circ$

Answer

D) $144^\circ$

Question 16

In $ riangle XYZ$, side YZ is extended to point $W$.

If exterior angle $\angle XZW = 120^\circ$ and interior angle $\angle Y = 2\angle X$, find the measure of $\angle X$.

Accepted Answer

B) $40^\circ$

Answer

A) $30^\circ$

Answer

C) $60^\circ$

Answer

D) $80^\circ$

Question 17

Five rays OA, OB, OC, OD, OE meet at a common point $O$.

If $\angle AOB = x^\circ$, $\angle BOC = (2x)^\circ$, $\angle COD = (3x)^\circ$, $\angle DOE = (4x)^\circ$, and $\angle EOA = (5x)^\circ$, find the measure of the largest angle.

Accepted Answer

C) $120^\circ$

Answer

A) $24^\circ$

Answer

B) $96^\circ$

Answer

D) $144^\circ$

Question 18

Lines PQ and RS intersect at point $O$.

If $\angle POR : \angle ROQ = 5 : 7$, find the measure of all four angles around $O$.

Accepted Answer

A) $75^\circ, 105^\circ, 75^\circ, 105^\circ$

Answer

B) $60^\circ, 120^\circ, 60^\circ, 120^\circ$

Answer

C) $50^\circ, 130^\circ, 50^\circ, 130^\circ$

Answer

D) $80^\circ, 100^\circ, 80^\circ, 100^\circ$

Question 19

Through vertex $A$ of $ riangle ABC$, a line DAE is drawn parallel to base BC.

If $\angle DAB = 50^\circ$ and $\angle EAC = 65^\circ$, find $\angle BAC$ and $\angle ACB$.

Accepted Answer

A) $\angle BAC = 65^\circ, \angle ACB = 65^\circ$

Answer

B) $\angle BAC = 50^\circ, \angle ACB = 65^\circ$

Answer

C) $\angle BAC = 65^\circ, \angle ACB = 50^\circ$

Answer

D) $\angle BAC = 55^\circ, \angle ACB = 60^\circ$

Question 20

Two parallel lines $l \parallel m$ are intersected by transversal $t$.

If a pair of alternate interior angles are given by $(2x + 30)^\circ$ and $(3x - 10)^\circ$, find $x$ and the measure of the co-interior angle on the same side.

Accepted Answer

A) $x = 40$, co-interior angle = $70^\circ$

Answer

B) $x = 30$, co-interior angle = $90^\circ$

Answer

C) $x = 40$, co-interior angle = $110^\circ$

Answer

D) $x = 50$, co-interior angle = $50^\circ$

Grade 9 : Mathematics - 5. Lines and Angles (Set 3)