Class 9 Chapter 8: Quadrilaterals - Competitive Exam Practice Set
Welcome, future achievers! Class 9 Chapter 8 (Quadrilaterals) is a cornerstone of Geometry, heavily featured in competitive exams like SSC CGL/CHSL/MTS, RRB NTPC/Group D, and SSC GD Constable. To help you master this high-scoring topic, we have curated previous year questions (PYQs) and exam-targeted problems. Practice these questions, learn the shortcut tricks, and boost your accuracy!
Q1. The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find the measure of the smallest angle. (SSC GD / MTS PYQ)
• Property: The sum of all interior angles of a quadrilateral is 360°.
• Let the angles be 3x, 5x, 9x, and 13x.
• 3x + 5x + 9x + 13x = 360° ⇒ 30x = 360° ⇒ x = 12°.
• Smallest angle = 3x = 3 × 12° = 36°.
• Shortcut: Sum of ratios = 30 units. 30 units = 360° ⇒ 1 unit = 12°. Smallest ratio is 3 units = 3 × 12 = 36°.
Correct Answer: B
Q2. In a parallelogram ABCD, if adjacent angles ∠A = (2x + 15)° and ∠B = (3x - 10)°, find the value of x. (RRB NTPC PYQ)
• Property: Adjacent angles of a parallelogram are supplementary (sum is 180°).
• ∠A + ∠B = 180° ⇒ (2x + 15) + (3x - 10) = 180
• 5x + 5 = 180 ⇒ 5x = 175 ⇒ x = 35.
Correct Answer: A
Q3. The diagonals of a rhombus are 16 cm and 12 cm. Find its perimeter. (SSC CHSL / CGL PYQ)
• Property: Diagonals of a rhombus bisect each other at right angles (90°).
• Half of diagonals are 8 cm (16/2) and 6 cm (12/2).
• Side of rhombus (using Pythagoras theorem in the small triangle): Side = √(8² + 6²) = √(64 + 36) = √100 = 10 cm.
• Perimeter = 4 × Side = 4 × 10 = 40 cm.
• Shortcut: Recognize the 3-4-5 Pythagorean triplet scaled by 2 (6-8-10). The side must be 10 cm. Perimeter = 40 cm.
Correct Answer: C
Q4. In ▵ABC, D and E are the midpoints of sides AB and AC respectively. If DE = 5.6 cm, then what is the length of BC? (SSC MTS PYQ)
• Midpoint Theorem: The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.
• Therefore, DE = ½ BC ⇒ BC = 2 × DE.
• BC = 2 × 5.6 cm = 11.2 cm.
Correct Answer: B
Q5. In a trapezium ABCD, AB || CD. If ∠A = 55° and ∠B = 70°, find the values of ∠D and ∠C. (RRB Group D PYQ)
• Since AB || CD, the consecutive interior angles on the same side of the transversal are supplementary.
• ∠A + ∠D = 180° ⇒ 55° + ∠D = 180° ⇒ ∠D = 180° - 55° = 125°.
• ∠B + ∠C = 180° ⇒ 70° + ∠C = 180° ⇒ ∠C = 180° - 70° = 110°.
Correct Answer: A
Excellent effort on completing the Chapter 8 Revision Quiz! Quadrilaterals is a highly visual chapter, and mastering core properties such as the Angle Sum Property, properties of Special Parallelograms, and the Midpoint Theorem can save you precious seconds during examinations. Keep revising, practice regularly, and check out our other free daily practice worksheets for SSC, RRB, and GD exams!
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