Geometry

65°

Step 1: Two angles are complementary means their sum = 90°. Step 2: One angle = 35°, let the other angle = x. Step 3: 35° + x = 90°. Step 4: x = 90° - 35°. Final Step: x = 55°. Wait - let me recheck: 90 - 35 = 55°. The correct answer is 55°. Common mistake: confusing complementary (sum = 90°) with supplementary (sum = 180°).

60°

Step 1: The angle at the centre = 120°. We need to find the angle at the circumference. Step 2: By Theorem 10, the angle subtended by an arc at the centre is double the angle subtended at any point on the remaining circumference. Step 3: Angle at centre = 2 × Angle at circumference. Step 4: 120° = 2 × Angle at circumference. Final Step: Angle at circumference = 120° ÷ 2 = 60°.

65°

Step 1: In a parallelogram, consecutive (adjacent) angles are supplementary, meaning they add up to 180°. Step 2: One angle = 115°, let the adjacent angle = x. Step 3: 115° + x = 180°. Step 4: x = 180° - 115°. Final Step: x = 65°. Remember: opposite angles are equal, adjacent angles are supplementary in a parallelogram.

360°

Step 1: We need to find the sum of interior angles of a quadrilateral (4 sides). Step 2: Using the formula: Sum of interior angles = (n - 2) × 180°, where n = number of sides. Step 3: For a quadrilateral, n = 4. So sum = (4 - 2) × 180°. Step 4: Sum = 2 × 180° = 360°. Final Step: The sum of all interior angles of a quadrilateral is 360°. This can also be verified by dividing the quadrilateral into 2 triangles, each with 180°.