Class 9 Practice – Level 1 – Lines and Angles

Total questions: 40

In the figure, lines AB and CD intersect at O. If angle AOC + angle BOE =70 and angle BOD = 40, find angle BOE and reflex angle COE.

Topic: Intersecting Lines and Angles

$\displaystyle {{45}^{{^{\circ }}}}$

$\displaystyle {{30}^{{^{\circ }}}}$

$\displaystyle {{60}^{{^{\circ }}}}$

$\displaystyle {{35}^{{^{\circ }}}}$

None

In the figure lines XY and MN intersect at O. If angle POY = $\displaystyle {{90}^{{^{\circ }}}}$ and a : b = 2 : 3, what is the value of c.

Topic: Intersecting Lines and Angles

$\displaystyle {{90}^{{^{\circ }}}}$

$\displaystyle {{60}^{{^{\circ }}}}$

$\displaystyle {{126}^{{^{\circ }}}}$

$\displaystyle {{130}^{{^{\circ }}}}$

None

In Fig , $\displaystyle \angle PQR=\angle PRQ,\text{ then prove that }\angle PQS=\angle PRT.$

Topic: Properties of Isosceles Triangles

$\displaystyle \angle PQS=\angle PRT$

$\displaystyle \angle PQR=\angle PRQ$

$\displaystyle \angle PWR=\angle PRQ$

$\displaystyle \angle PQR=\angle PQS$

None

As shown in the figure find x and y if $\displaystyle \angle ACB=100{}^\circ ,\angle ADE={{120}^{{^{\circ }}}}$

Topic: Angle Relationships in Triangles and Lines

$\displaystyle x={{80}^{{^{\circ }}}}\text{ and }y={{40}^{{^{\circ }}}}$

$\displaystyle x={{50}^{{^{\circ }}}}\text{ and }y={{40}^{{^{\circ }}}}$

$\displaystyle x={{80}^{{^{\circ }}}}\text{ and }y={{60}^{{^{\circ }}}}$

$\displaystyle x={{80}^{{^{\circ }}}}\text{ and }y={{90}^{{^{\circ }}}}$

None

$\displaystyle \text{In }\vartriangle ABC,\angle A+\angle B={{65}^{{^{\circ }}}}and\angle B+\angle C={{140}^{{^{\circ }}}}$ find the measure of each angle of the triangle.

Topic: Sum of angles in a triangle

$\displaystyle {{80}^{{^{\circ }}}},{{25}^{{^{\circ }}}}\text{ and }{{115}^{{^{\circ }}}}.$

$\displaystyle {{40}^{{^{\circ }}}},{{25}^{{^{\circ }}}}\text{ and }{{115}^{{^{\circ }}}}.$

$\displaystyle {{40}^{{^{\circ }}}},{{25}^{{^{\circ }}}}\text{ and }{{125}^{{^{\circ }}}}.$

$\displaystyle {{40}^{{^{\circ }}}},{{135}^{{^{\circ }}}}\text{ and }{{115}^{{^{\circ }}}}.$

None

Find the value of $\displaystyle x$.

Topic: Angle Relationships

$\displaystyle {{115}^{{^{\circ }}}}$

$\displaystyle {{95}^{{^{\circ }}}}$

$\displaystyle {{110}^{{^{\circ }}}}$

$\displaystyle {{100}^{{^{\circ }}}}$

None

In Fig., the sides AB and AC of ΔABC are produced to points E and D respectively. If bisectors BO and CO of ∠CBE and ∠BCD respectively meet at point O, then prove that ∠BOC=90°- $\displaystyle \dfrac{1}{2}$ ∠BAC.

Topic: Angle Bisector Theorem and Angle Properties in Triangles

$\displaystyle {{90}^{\circ }}$

$\displaystyle {{95}^{\circ }}$

$\displaystyle {{105}^{\circ }}$

$\displaystyle {{85}^{\circ }}$

None

Find the supplement of the following angle: $\displaystyle {{90}^{\circ }}$

Topic: Supplementary Angles

$\displaystyle {{45}^{\circ }}$

$\displaystyle {{60}^{\circ }}$

$\displaystyle {{90}^{\circ }}$

$\displaystyle {{70}^{\circ }}$

None

Find the measure of an angle which is 36° more than its complement.

Topic: Complementary Angles

63°

45°

78°

33°

None

10.

Two complementary angles are in the ratio 4:5. Find the angles.

Topic: Complementary Angles

10°, 80°

20°, 70°

30, 60°

40°, 50°

None

11.

If the supplement of an angles is three times its complement, then the angle is ?

Topic: Supplementary and Complementary Angles

45°

40°

80°

70°

None

12.

Angle between the hours and minute hand of a clock at 11 :15 is -

Topic: Clock Angles

90°

112.5°

120°

80°

None

13.

In figure, sides QP and RQ of △PQR are produced to points S and T respectively. If ∠SPR=135° and ∠PQT=110°,∠PRQ= ?

Topic: Angles in Triangles

85°

75°

65°

95°

None

14.

In figure, if AB∥DE,∠BA C= 35° and ∠CDE= 53° ,∠DCE = ?

Topic: Angles with Parallel Lines

106°

92°

105°

15°

None

15.

In figure, if AB ∥ CD ,CD ∥ EF and 𝑦 : 𝑧 = 3 : 7, 𝑥 = ?

Topic: Angles with Parallel Lines (Multiple Lines)

126°

166°

146°

136°

None

16.

In the given figure, if PQ∥RS, ∠MXQ=135° and ∠MYR=40° ,then the value of ∠XMY is

Topic: Properties of Parallel Lines and Angles

35°

85°

75°

45°

None

17.

The angles of a triangle are ( 𝑥 − 40)° ,( 𝑥 − 20)° and ($\displaystyle \dfrac{1}{2}$𝑥 −10)°. Then the value of 𝑥 is

Topic: Angles in Triangles

95°

100°

50°

60°

None

18.

Compute the value of 𝑥 in the given figure.

Topic: Angle Calculation

44°

45°

35°

65°

None

19.

Compute the value of 𝑥 in the given figure.

Topic: Angle Calculation

40°

50°

60°

45°

None

20.

Compute the value of 𝑥 in the given figure.

Topic: Angle Calculation

88°

44°

100°

120°

None

21.

Find the angle which is complement of itself.

Topic: Complementary Angles

45°

35°

65°

75°

None

22.

If the angle (2𝑥−10)° and ( 𝑥−5)° are complementary angles, find 𝑥.

Topic: Complementary Angles

45°

35°

105°

75°

None

23.

OA and OB are opposite rays. If 𝑥=75°,what is the value of 𝑦?

Topic: Opposite Rays

25°

125°

105°

95°

None

24.

OA and OB are opposite rays. If 𝑦=110°, what is the value of 𝑥?

Topic: Opposite Rays

90°

50°

80°

70°

None

25.

If two angles are complementary of each other, then each angle is :

Topic: Complementary Angles

An Obtuse angle

A Right angle

An Acute angle

A supplementary angle.

None

26.

X lies in the interior of ∠BAC. If ∠BAC=70° and ∠BAX=42° then ∠XAC= ?

Topic: Angle Bisector and Angle Relationships

70°

45°

30°

28°

None

27.

An angle is 14° more than its complementary angle, then angle is :

Topic: Complementary Angles

14°

38°

50°

52°

None

28.

If two are intersected by a transversal, then each pair of corresponding angles so formed is :

Topic: Corresponding Angles

Equal

Complementary

Supplementary

None of these

None

29.

Two parallel lines have :

Topic: Properties of Parallel Lines

A common point

Two common points

No common point

Infinite common points

None

30.

If two parallel lines are intersected by transversal then the bisectors of the interior angles form a :

Topic: Angle Bisectors of Parallel Lines

Rhombus

∥gm

Square

Rectangle

None

31.

If ℓ is any given line and P is any point not lying on ℓ, then the number of parallel lines than can through P, parallel to ℓ would be :

Topic: Parallel Lines

One

Two

Infinite

None of these

None

32.

The supplementary angle of the complementary of 30° is:

Topic: Supplementary and Complementary Angles

60°

120°

30°

150°

None

33.

A triangle can have:

Topic: Properties of Triangles

Two right angles

Two obtuse angle

all angles more than 60º

Two acute angles

None

34.

In the adjoining figure, AOB is a straight line. Find the value of 𝑥.

Topic: Linear Pair of Angles

25°

115°

75°

45°

None

35.

Which of the following statements is false?

Topic: Triangle Properties

A line segment can be produced to any desired length.

Through a given point, only one straight line can be drawn.

Through two given points, it is possible to draw one and only one straight line.

Two straight lines can intersect in only one point.

None

36.

In the adjoining figure PQ∣∣RS find 𝑥 = and y.

Topic: Parallel Lines and Angles

𝑥 = 55°, y = 40°

𝑥 = 85°, y = 25°

𝑥 = 75°, y = 35°

𝑥 = 45°, y = 45°

None

37.

In the given figure if AB∣∣DC and ∠BDC=30°∠BAD=80° find ∠x, ∠y, ∠z.

Topic: Angles in Parallel Lines and Transversals

𝑥 = 30°, 𝑦 = 70°, 𝑧 = 110°

𝑥 = 50°, 𝑦 = 60°, 𝑧 = 120°

𝑥 = 10°, 𝑦 = 80°, 𝑧 = 150°

𝑥 = 35°, 𝑦 = 75°, 𝑧 = 130°

None

38.

In Fig., the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then ∠QTR=$ \displaystyle \dfrac{1}{2}$ ∠QPR.

Topic: Exterior Angle Bisectors of a Triangle