Geometry · SSC CGL previous year questions

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2025 53 questions

Q722025 · 21 Sept 2025 · Shift 3
The sum of all interior angles of a 20-sided polygon is:
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: A
Q752025 · 21 Sept 2025 · Shift 3
A right-angled triangle ABC has legs AB=6 cm and BC=8 cm. An altitude BD is drawn from the vertex B to the hypotenuse AC. What is the length of the altitude BD?
1. A.4.8 cm
2. B.5.6 cm
3. C.6.4 cm
4. D.7.2 cm
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Answer: A
Q692025 · 20 Sept 2025 · Shift 1
When a transversal intersects two parallel lines, one of the alternate interior angles is 115°. What is the measure of the angle that lies opposite to it on the alternate interior side?
1. A.65°
2. B.90°
3. C.180°
4. D.115°
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Answer: D
Q692025 · 20 Sept 2025 · Shift 3
Two parallel lines are intersected by a transversal. If a pair of corresponding angles is formed, and one of the angles measures 130°, what is the measure of the other angle?
1. A.50°
2. B.90°
3. C.130°
4. D.180°
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Answer: C
Q682025 · 19 Sept 2025 · Shift 1
A parallelogram is a quadrilateral in which:
1. A.Only one pair of opposite sides is parallel.
2. B.All four interior angles are 90°.
3. C.Opposite sides are parallel and of equal length.
4. D.The diagonals are perpendicular.
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Answer: C
Q702025 · 19 Sept 2025 · Shift 1
In a quadrilateral ABCD, a line segment BD is a diagonal such that AB = CD and $∠ A B D = ∠ C D B$ . Are the triangles ABD and CDB congruent? If so, by what rule?
1. A.Yes, by SSS
2. B.Yes, by SAS
3. C.Yes, by ASA
4. D.No, they are not congruent
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Answer: B
Q602025 · 19 Sept 2025 · Shift 2
A wheelchair ramp needs to reach a platform that is 1.5 metres high. If the ramp is designed to make an angle of 30° with the level ground, what is the length of the ramp?
1. A.1.5 m
2. B.2 m
3. C.2.5 m
4. D.3 m
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Answer: D
Q672025 · 19 Sept 2025 · Shift 2
If every exterior angle of a regular polygon is 60°, how many sides does the polygon have?
1. A.4
2. B.5
3. C.6
4. D.8
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Answer: C
Q682025 · 19 Sept 2025 · Shift 2
In a triangle PQR, the centroid is at G(1, 2). If the vertices P and Q are at (3, -1) and (-2, 4) respectively, what are the coordinates of vertex R?
1. A.(2, 5)
2. B.(2, 4)
3. C.(1, 3)
4. D.(2, 3)
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Answer: D
Q592025 · 19 Sept 2025 · Shift 3
A ladder reaches a window 8 meters high on a vertical wall. If the ladder is positioned at a 45° angle to the ground, what is its length? (nearest to a whole number)
1. A.10 m
2. B.11 m
3. C.12 m
4. D.13 m
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Answer: B
Q682025 · 19 Sept 2025 · Shift 3
A regular polygon has each interior angle measuring 150°. Find the number of its sides.
1. A.10
2. B.12
3. C.15
4. D.18
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Answer: B
Q702025 · 19 Sept 2025 · Shift 3
In $△ A B C$ , an angle bisector from A meets BC at D. If AD bisects $∠ B A C$ , and AB = AC, are $△ A B D$ and $△ A C D$ congruent? If so, by what rule?
1. A.Yes, by SSS
2. B.Yes, by SAS
3. C.Yes, by ASA
4. D.No, they are not congruent
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Answer: B
Q612025 · 18 Sept 2025 · Shift 1
A vertical pole TF has its base F on the ground. From a point A, 25 metres from F, the angle of elevation of T is x°. From another point B, 75 metres from F (and in the same line as A), the angle of elevation of T is y°. If the height of the pole is $253$ metres, what is the value of x° + y°?
1. A.60°
2. B.75°
3. C.90°
4. D.120°
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Answer: C
Q682025 · 18 Sept 2025 · Shift 1
Triangle ABC has its centroid at point G(4, 5), and vertex A is located at (2, 3). If point D is the midpoint of side BC, what are the coordinates of D?
1. A.(5, 6)
2. B.(5, 8)
3. C.(6, 7)
4. D.(6, 8)
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Answer: A
Q592025 · 18 Sept 2025 · Shift 2
A rock climber uses a rope to ascend a cliff. If the vertical height of the cliff is 35 meters and the rope makes an angle of 30° with the level ground, what is the minimum length of the rope required to reach the top?
1. A.35 m
2. B.40 m
3. C.60 m
4. D.70 m
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Answer: D
Q652025 · 18 Sept 2025 · Shift 2
A tower generates a shadow that is 40 meters long when the sun's angle of elevation is 45 degrees. What is the height of the tower?
1. A.50 m
2. B.40 m
3. C.20 m
4. D.10 m
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Answer: B
Q682025 · 18 Sept 2025 · Shift 2
What is the measure of each interior angle in a regular eight-sided polygon?
1. A.120°
2. B.135°
3. C.150°
4. D.165°
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Answer: B
Q612025 · 18 Sept 2025 · Shift 3
A statue that is 1.6 metres in height is positioned on top of a pedestal. From a location on the ground, the angle of elevation to the top of the statue measures 60 degrees, while the angle of elevation to the top of the pedestal from the same point is 45 degrees. Determine the height of the pedestal.
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: C
Q672025 · 18 Sept 2025 · Shift 3
The sum of the exterior angles of a polygon is:
1. A.180°
2. B.360°
3. C.540°
4. D.720°
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Answer: B
Q592025 · 17 Sept 2025 · Shift 1
A flagpole has a shadow measuring 10 meters. Given that the height of the flagpole is $103$ meters, what is the angle at which the sun is elevated?
1. A.30°
2. B.45°
3. C.60°
4. D.75°
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Answer: C
Q682025 · 17 Sept 2025 · Shift 1
A triangle can have:
1. A.Two right angles
2. B.One obtuse angle and one right angle
3. C.Only one right or one obtuse angle
4. D.Three acute angles each measuring more than 60°
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Answer: C
Q592025 · 17 Sept 2025 · Shift 3
A taut wire supports a vertical pole. The wire is fixed to the ground 10 meters away from the base of the pole and makes an angle of 60° with the ground. What is the length of the wire?
1. A.Option 1
2. B.Option 2
3. C.Option 3
4. D.Option 4
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Answer: C
Q682025 · 17 Sept 2025 · Shift 3
What is the total measure of all interior angles in a ten-sided polygon?
1. A.540°
2. B.1440°
3. C.720°
4. D.900°
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Answer: B
Q682025 · 16 Sept 2025 · Shift 3
The angle bisectors of triangle ABC converge at the incenter I. Given that the measure of ∠BIC is 125°, what is the measure of ∠BAC?
1. A.50°
2. B.70°
3. C.80°
4. D.100°
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Answer: B
Q692025 · 16 Sept 2025 · Shift 3
In a quadrilateral ABCD, AB is parallel to CD, and AC is a diagonal. If AB = CD, which of the following is true?
1. A.△ABC ≅ △CDA by SSS
2. B.△ABC ≅ △CDA by SAS
3. C.△ABC ≅ △CDA by ASA
4. D.The triangles are similar, but not necessarily congruent
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Answer: B