Quadrilaterals

Answer

Step 1: Use angle sum property of quadrilateral → Sum of all angles = 360°. Step 2: ∠A + ∠B + ∠C + ∠D = 360°. Step 3: 85° + 95° + 75° + ∠D = 360°. Step 4: 255° + ∠D = 360°. Step 5: ∠D = 360° - 255° =

Answer

Step 1: In parallelogram, opposite angles are equal → ∠R = ∠P = 65°. Step 2: Adjacent angles are supplementary → ∠P + ∠Q = 180°. Step 3: 65° + ∠Q = 180° → ∠Q = 115°. Step 4: ∠S = ∠Q = 115° (opposite a

Answer

Step 1: In parallelogram, opposite sides are equal. Step 2: If adjacent sides are 8 cm and 12 cm, then all four sides are: 8 cm, 12 cm, 8 cm, 12 cm. Step 3: Perimeter = sum of all sides = 8 + 12 + 8 +

Answer

Step 1: Use midpoint theorem → Line joining midpoints of two sides is parallel to third side and half its length. Step 2: DE || BC and DE = (1/2) × BC. Step 3: DE = (1/2) × 16 = 8 cm. Answer: DE = 8 c

Answer

Step 1: In parallelogram, diagonals bisect each other. Step 2: O is midpoint of both diagonals. Step 3: AO = (1/2) × AC = (1/2) × 10 = 5 cm. Step 4: BO = (1/2) × BD = (1/2) × 14 = 7 cm. Answer: AO = 5

Answer

Step 1: Given ABCD with diagonals AC, BD intersecting at O where AO = OC, BO = OD. Step 2: In triangles AOB and COD: AO = OC (given), BO = OD (given), ∠AOB = ∠COD (vertically opposite). Step 3: △AOB ≅

Answer

Step 1: Rectangle has all angles = 90°. Step 2: Apply Pythagoras theorem in right triangle ABC. Step 3: AC² = AB² + BC². Step 4: AC² = 12² + 9² = 144 + 81 = 225. Step 5: AC = √225 = 15 cm. Answer: AC

Answer

Step 1: In rhombus, diagonals bisect at right angles. Step 2: Let diagonals intersect at O. PO = 12 cm, SO = QS/2. Step 3: In right triangle POS: PS² = PO² + SO². Step 4: 13² = 12² + SO². Step 5: 169