Geometry Test

Result

Geometry Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

In the given figure, two lines AB and CD intersect at O and BOE = 66°.

What is the measure of AOC?

A
75°

B
85°

C
114°

D
19°

Solution

BOC + AOC = 180° [Linear pair]
5x° + AOC = 180° … (i)
Also, BOC + BOE + EOD = 180° [Linear pair]
5x° + 66° + x° = 180°
6x° = 180° - 66°
6x° = 114°
x° = 19°
5x = 95°
∴ AOC = 180° - 95°
AOC = 85°
Question 2
1 / -0

For what value of x, will P and P' coincide?

A
20°

B
40°

C
30°

D
50°

Solution

P and P¢ will coincide only if
3x – 20 + 4x – 10 = 180°
7x – 30 = 180°
7x = 210°
x =
∴ When x = 30°, points P and P¢ will coincide.
Question 3
1 / -0

In the figure, AB is a mirror, MO is an incident ray and ON is the reflected ray. If MON = 124°, what will be the value of AOM?

A
62°

B
28°

C
56°

D
38°

Solution

MON = 124°
Also AOM = BON [∵ Angle of incidence = Angle of reflection]
∴ 2AOM = 180° – 124°
AOM =
Question 4
1 / -0

In the given figure, if PQ || RS, what is the value of x?

A
70°

B
110°

C
100°

D
30°

Solution

As PQ || RS,
x + 70° = 180° [Co-interior angles]
x = 110°
Question 5
1 / -0

If AB || CD, EF is a transversal and OP bisects EOB, what is the value of x?

A
80°

B
140°

C
100°

D
50°

Solution

It is given that EOB = 2POB
EOB = 2 × 40° = 80°
x = 180° – EOB
x = 180° – 80°
x = 100°
Question 6
1 / -0

If AB || CD and OP⊥AB, what is the value of x°?

A
90°

B
55°

C
125°

D
75°

Solution

PBQ = DQB= x [Alternate interior angles]
Also, 180°- DQB = 125°(Linear Pair)180° - x° = 125°x° = 180° - 125°x° = 55°
Question 7
1 / -0

If AX || CY, what is the measure of ABP?

A
80°

B
260°

C
100°

D
140°

Solution

Construction: Draw ZB || YC || XA
1 + 120° = 180°
and 2 + 140° = 180° [Co-interior angles]
1 = 60° and 2 = 40°
1 + 2 = 100°
∴ ABP = 180° – (1 + 2) = 80°
Question 8
1 / -0

If PQ || RS, what is the value of a?

A
136°

B
68°

C
112°

D
40°

Solution

Construction: Draw XZ || PQ || RS
1 = 180° – 104° = 76°
2 = 180° – 120° = 60°
PYR = 1 + 2 = 136°
Reflex PYR = 360° – PYR
= 360° – 136°
= 224°
Now in concave quadrilateral PXRY:
a + 36° + 224° + 32° = 360°
a = 360° – 292°
a = 68°
Question 9
1 / -0

If AB || CD, EF || CD, ABC = 70° and CEF = 120°, what is the value of a?

A
10°

B
15°

C
20°

D
30°

Solution

ECD = 180° – 120° = 60°
Also, ABC = BCD = 70°
And a° = BCD – ECD
= 70° – 60° = 10°
Question 10
1 / -0

If || m || n and AB || DC, then what is the value of x?

A
105°

B
145°

C
125°

D
85°

Solution

1 = 2 as AB || CD
2 + 35° = 70° [Vertically opposite angles]
2 = 35°
∴ 1 = 35°
Now, x + 1 = 180° [Linear pair]
x = 180° - 35°
= 145°
Question 11
1 / -0

If PQ || RS, what is the value of x?

A
90°

B
130°

C
150°

D
70°

Solution

1 + 110° = 180°
1 = 70°
Also, 1 = 2 + 20° [Exterior angle property]
2 = 50°
x + 2 = 180°
x = 180° – 50°
= 130°
Question 12
1 / -0

In ΔABC, if 2A = 3B = 6C, find the measure of B.

A
30°

B
90°

C
60°

D
45°

Solution

In ΔABC: A + B + C = 180°
B + B + B = 180°
B
B =
Question 13
1 / -0

In the figure, if || m, p || q, DAC = 30° and ABC = 70°, then what is the measure of ACD?

A
70°

B
80°

C
110°

D
150°

Solution

According to the data given in the question, || m and AC is a transversal.
∴ DAC = ACB [Alternate interior angles]
ACB = 30°
Also, q is a transversal.
∴ ABC + BCD = 180° [Co-interior angles]
70° + BCD = 180°
BCD = 110°
Now, ACB + ACD = BCD
30° + ACD = 110°
ACD = 110° - 30° = 80°
Hence, 80° is the correct answer.
Question 14
1 / -0

In the figure, if || m || n and x = 125°, then what is the value of (z° - y°)?

A
70°

B
80°

C
85°

D
180°

Solution

1 + x° = 180° (Linear pair)
1 = 180° - x = 180° - 125°
1 = 55°
|| m and q is a transversal.
1 = y° [Alternate interior angles]
y = 55°
Now, y° + 2 = 180° (Linear pair)
2 = 180° - y°
2 = 180° - 55°
2 = 125°
Now, m || n and q is a transversal.
2 = z° (Alternate interior angles]
z° = 125°
Now, z° - y° = 125° - 55° = 70°
Hence, (1) is the correct option.
Question 15
1 / -0

Which of the following conditions would make || m?

A
2 > 1

B
2 = 1

C
2 < 1

D
2 = 180° – 1

Solution

Since 1 and 2 form corresponding angles, so 1 should be equal to 2 to make || m.
Hence, (2) is the correct option.