Quadrilaterals — Flashcards
ICSE · Class 6 · Mathematics
26 flashcards for Quadrilaterals (ICSE Class 6 Mathematics) to test yourself on key terms and facts. Sample: "The three angles of a quadrilateral are 75°"
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The three angles of a quadrilateral are 75°, 85°, and 100°. Find the fourth angle.
Answer
Step 1: Sum of all angles in a quadrilateral = 360° Step 2: Add given angles → 75° + 85° + 100° = 260° Step 3: Subtract from 360° → 360° − 260° = 100° Answer: The fourth angle is 100°.
In a quadrilateral, angles are in the ratio 2:3:4:5. Find each angle.
Answer
Step 1: Total parts = 2 + 3 + 4 + 5 = 14 Step 2: Total angle sum = 360° Step 3: Each part = 360° ÷ 14 = 25.71° (approx) Step 4: Angles → - 2 × 25.71 ≈ 51.43° - 3 × 25.71 ≈ 77.14° - 4 × 25.71 ≈ 102.86°…
Three angles of a quadrilateral are equal. The fourth angle is 60°. Find the equal angles.
Answer
Step 1: Let each equal angle = x Step 2: Sum → x + x + x + 60° = 360° Step 3: 3x = 300° → x = 100° Answer: Each equal angle is 100°.
In a quadrilateral, ∠A = 2x, ∠B = 3x, ∠C = 4x, and ∠D = x. Find all angles.
Answer
Step 1: Sum → 2x + 3x + 4x + x = 360° Step 2: 10x = 360° → x = 36° Step 3: Angles → - ∠A = 2 × 36 = 72° - ∠B = 3 × 36 = 108° - ∠C = 4 × 36 = 144° - ∠D = 36° Answer: 72°, 108°, 144°, and 36°.
In a trapezium ABCD, AB || DC. If ∠A = 80°, find ∠D.
Answer
Step 1: AB || DC and AD is transversal → co-interior angles Step 2: ∠A + ∠D = 180° Step 3: 80° + ∠D = 180° → ∠D = 100° Answer: ∠D = 100°.
In a trapezium ABCD, AB || DC. If ∠B = 110°, find ∠C.
Answer
Step 1: AB || DC and BC is transversal → co-interior angles Step 2: ∠B + ∠C = 180° Step 3: 110° + ∠C = 180° → ∠C = 70° Answer: ∠C = 70°.
In an isosceles trapezium, ∠A = 75°. Find ∠B, ∠C, and ∠D.
Answer
Step 1: In isosceles trapezium, base angles are equal → ∠A = ∠B = 75° Step 2: ∠A + ∠D = 180° → 75° + ∠D = 180° → ∠D = 105° Step 3: ∠C = ∠D = 105° Answer: ∠B = 75°, ∠C = 105°, ∠D = 105°.
In a parallelogram, one angle is 100°. Find the other three angles.
Answer
Step 1: Opposite angles are equal → one opposite angle = 100° Step 2: Adjacent angles are supplementary → other two angles = 180° − 100° = 80° Step 3: Opposite of 80° is also 80° Answer: 100°, 80°, 10…
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