MCQ

MCQ 11 Mark

In the given figure, PA || BC || DQ and AB || DC. Then the values of x and y are respectively :

A
50°, 120°
B
50°, 130°
C
60°, 120°
D
60°, 130°

Answer

In the given figure,
PA || BC || DQ
AB || DC
x = 50° (Alternate angles)
∠BCD + ∠ABC = 180° (Sum of co-interior angles)
⇒ ∠DCB + 50° = 180°
⇒ ∠DCB = 180° – 50° = 130°
BC || DQ
∠DCB = ∠CDQ (Alternate angles)
y = 130°
x = 50°, y = 130° (b)

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MCQ 21 Mark

In the given figure, AB || CD. If ∠APQ = 50° and ∠PRD = 130°, then ∠QPR is

A
30°
B
50°
C
80°
D
130°

Answer

In the given figure,
AB || CD, ∠APQ = 50°
∠PRD = 130°, ∠QPR = ?
AB || CD
∠APQ = ∠PQR (Alternate angles)
∠PQR = 50°
∠PRD + ∠PRQ = 180° (Linear pair)
130° + ∠PRQ = 180°
∠PRQ = 180° – 130° = 50°
Now in ∆PQR
∠PQR + ∠PRQ + ∠QPR = 180° (Angles of a triangle)
50° + 50° + ∠QPR = 180°
∠QPR = 180° – 50° – 50° = 80° $\text{(c)}$

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MCQ 31 Mark

In the gitsen figure, if l || m then the value of x is

A
x = 75°
B
x = 95°
C
x = 105°
D
x = 115°

Answer

In the given figure, l || m
∠1 = 75° (Vertically opposite angles)
and ∠1 + x = 180° (Co-interior angles)
x + 75° = 180°
x = 180° – 75° = 105° $\text{(c)}$

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MCQ 41 Mark

In the given figure, if l || m then the value of x is

A
x = 50
B
x = 60
C
x = 70
D
x = 45

Answer

In the given figure, l || m
110° = 3x – 40°
⇒ 3x = 110° + 40° = 150°
x = 50° (a)

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MCQ 51 Mark

If two lines are intersected by a transversal, then the number of pairs of interior angles on the same side of transversal is

Answer

Two lines are intersected by a transversal then a number of pairs of interior angles on the same side of the transversal is two. (b)

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MCQ 61 Mark

In the given figure, the value of x that will make AOB a straight line is

A
x = 40
B
x = 35
C
x = 30
D
x = 25

Answer

AOB will be a straight line if
3x + 15 + 2x – 10° = 180°
⇒ 5x + 5 = 180°
⇒ 5x = 180° – 5 = 175°
⇒ x = 35° (b)

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MCQ 71 Mark

If one angle of a linear pair is acute, then the other angle is

A
acute
B
obtuse
C
right
D
straight

Answer

If one angle of a linear pair is acute,
then the other angle will be obtuse.
(∵ Linear pair = 180°) (b)

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MCQ 81 Mark

If an angle measures $10^{\circ}$ more than its complement, then the measure of the angle is

A
$40^{\circ}$
B
$55^{\circ}$
C
$35^{\circ}$
D
$50^{\circ}$

Answer

If one angle measures $10^{\circ}$ more than its complement, then measure of the angle $=50^{\circ}$.
$\left(\because 50^{\circ}+40^{\circ}=90^{\circ}\right)$

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MCQ 91 Mark

If an angle is one-third of its supplement, then the measure of the angle is

A
$45^{\circ}$
B
$30^{\circ}$
C
$135^{\circ}$
D
$150^{\circ}$

Answer

If one angle is one-third of its supplement, then the measure of an angle is $45^{\circ}$. (a)
Let first angle $=x^{\circ}$
$\frac{1}{3}$ of supplement $=\frac{1}{3} x$
Now, $\frac{x}{1}+\frac{1}{3} x=180^{\circ}$
$\begin{array}{c}
\frac{3 x+x}{3}=180^{\circ} \\
4 x=180^{\circ} \times 3 \\
x=\frac{180 \times 3}{4}=135^{\circ}
\end{array}$

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MCQ 101 Mark

A pair of supplementary angles is

A
$55^{\circ}, 115^{\circ}$
B
$65^{\circ}, 125^{\circ}$
C
$47^{\circ}, 133^{\circ}$
D
$40^{\circ}, 50^{\circ}$

Answer

A pair of supplementary angles is $47^{\circ}, 133^{\circ}$.
As the sum of supplementary angles is $180^{\circ}$. $\text{(c)}$

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MCQ 111 Mark

A pair of complementary angles is

A
$130^{\circ}, 50^{\circ}$
B
$35^{\circ}, 55^{\circ}$
C
$25^{\circ}, 75^{\circ}$
D
$27^{\circ}, 53^{\circ}$

Answer

A pair of complementary angles is $35^{\circ}, 55^{\circ}$.
As the sum of complementary angles is $90^{\circ}$. (b)

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