Calculating Angle Sums — Solutions

1. Triangle Warm-up

   1. x = 60° ▶ View Solution
   2. x = 45° — obtuse triangle ▶ View Solution
   3. x = 50° ▶ View Solution
   4. x = 64° ▶ View Solution
   5. Angles in ratio 1 : 2 : 3: 30°, 60°, 90° — right-angled triangle ▶ View Solution

2. The Right-Angled Property

   1. x = 60° ▶ View Solution
   2. x = 45° — isosceles triangle ▶ View Solution
   3. x = 78° ▶ View Solution
   4. Can a triangle have two right angles? No — two right angles sum to 180°, leaving 0° for the third ▶ View Solution
   5. Right-angled triangle with 37° — all three angles: 37°, 53°, 90° ▶ View Solution

3. Isosceles Triangle Logic

   1. Apex = 80°; base angles: 50° each ▶ View Solution
   2. Base angles = 55°; apex: 70° ▶ View Solution
   3. Apex = 120°; base angles: 30° each ▶ View Solution
   4. Base angles both 60°; apex: 60° — equilateral triangle ▶ View Solution
   5. Angles in ratio 3 : 3 : 2: 67.5°, 67.5°, 45° — isosceles triangle ▶ View Solution

4. The 360° Rule — Quadrilaterals

   1. x = 90° ▶ View Solution
   2. x = 60° ▶ View Solution
   3. x = 70° ▶ View Solution
   4. x = 30° ▶ View Solution
   5. 95° + 115° + 88° + x = 360°: 62° ▶ View Solution

5. Parallelograms

   1. Opposite angle to 70°: 70° ▶ View Solution
   2. Adjacent angle to 70°: 110° ▶ View Solution
   3. Two opposite angles sum to 200°; find all four: 100°, 100°, 80°, 80° ▶ View Solution
   4. Parallelogram with all equal angles; each angle: 90° — rectangle or square ▶ View Solution

6. Special Quadrilaterals

   1. x = 100° ▶ View Solution
   2. Isosceles trapezium; base angles = 75°; top angles: 105° each ▶ View Solution
   3. Parallelogram; two angles = 100°, one = 80°; fourth: 80° ▶ View Solution
   4. Can a quadrilateral have exactly three right angles? No — the fourth angle must also be 90° ▶ View Solution

7. Speed Round

   1. Sum of interior angles of two triangles: 360° ▶ View Solution
   2. Interior angle sum of a rectangle: 360° ▶ View Solution
   3. Square cut by diagonal — triangle angles: 90°, 45°, 45° ▶ View Solution
   4. Triangle with all sides equal; double classification: Equilateral and Acute ▶ View Solution

8. Visual Challenge

   1. x = 35° ▶ View Solution
   2. y = 65° ▶ View Solution
   3. x = 45° ▶ View Solution
   4. Verify angle sum of trapezium: 360° ✓ ▶ View Solution

9. The “What if?” Scenarios

   1. Triangle; angles in ratio 1 : 2 : 3: 30°, 60°, 90° — right-angled triangle ▶ View Solution
   2. Quadrilateral; all four angles equal: 90° each — rectangle or square ▶ View Solution
   3. Can an equilateral triangle have a 90° angle? No — impossible (all angles must be 60°) ▶ View Solution
   4. One angle of a square is 90°; can you determine all? Yes — all four angles are 90° ▶ View Solution

10. Mastery Check

    1. Does a diagonal prove 2 × 180° = 360° for a quadrilateral? True ▶ View Solution
    2. Isosceles triangle; exterior angle = 130°; base angles: 65° each ▶ View Solution
    3. Angles 105°, 38°, x; is this isosceles? x = 37° — scalene, not isosceles (38° ≠ 37°) ▶ View Solution