Calculating Angles (B) (With Clues) Worksheet | Printable Maths ... - Free Printable

I will solve the problem by calculating all the missing angles on this worksheet, using geometric principles. I'll work through each diagram systematically.

Diagram 1: Right-Angled Triangle

- a°: This is a right-angled triangle. The sum of angles in a triangle is 180°. One angle is 90°, another is 48°.
- Calculation: `a° = 180° - 90° - 48° = 42°`
- b°: This is the exterior angle at the same vertex as the 48° angle. An exterior angle equals the sum of the two opposite interior angles.
- Calculation: `b° = 90° + 42° = 132°`

Diagram 2: Parallelogram

- i°: Opposite angles in a parallelogram are equal. The given angle is 63°, so its opposite angle `i°` is also 63°.
- j°: Adjacent angles in a parallelogram are supplementary (add up to 180°).
- Calculation: `j° = 180° - 63° = 117°`
- k°: Opposite angles are equal, so `k° = j° = 117°`.

Diagram 3: Isosceles Triangle with Parallel Lines

- d°: The triangle is isosceles, and one base angle is 71°. Therefore, the other base angle `d°` is also 71°.
- e°: The line cuts across the triangle, creating corresponding angles. Since the top line is parallel to the base, `e°` is equal to the base angle `d°`.
- Calculation: `e° = 71°`
- f°: The sum of angles in a triangle is 180°.
- Calculation: `f° = 180° - 71° - 71° = 38°`
- c°: The line creates an alternate interior angle with the 71° angle, so `c° = 71°`.

Diagram 4: Kite or Irregular Quadrilateral

- l°: The sum of angles in a quadrilateral is 360°. We have three angles: 75°, 90° (right angle), and 63°.
- Calculation: `l° = 360° - 75° - 90° - 63° = 132°`

Diagram 5: Intersecting Lines (X-shape)

- g°: Vertically opposite angles are equal. The angle vertically opposite to `g°` is 82°, so `g° = 82°`.
- h°: Angles on a straight line add up to 180°. The angle adjacent to `h°` is 82°.
- Calculation: `h° = 180° - 82° = 98°`

Diagram 6: Right-Angled Triangle with Isosceles Triangle

- m°: The triangle is isosceles and right-angled. The two base angles are equal.
- Calculation: `m° = (180° - 90°) / 2 = 45°`
- n°: The angle `n°` is part of a straight line with the 68° angle and the 45° angle.
- Calculation: `n° = 180° - 68° - 45° = 67°`

Diagram 7: Triangle with Exterior Angle

- o°: The exterior angle is equal to the sum of the two opposite interior angles. The exterior angle is 118°, and one interior angle is 82°.
- Calculation: `o° = 118° - 82° = 36°`

Diagram 8: Complex Polygon (Arrow Shape)

- p°: The shape can be divided into triangles. The sum of angles in a pentagon is 540°. However, it's easier to see that `p°` is an exterior angle to a triangle with angles 94° and 90° (right angle).
- Calculation: `p° = 180° - (180° - 94° - 90°) = 94° + 90° = 184°` — This seems incorrect. Let me reconsider. The angle `p°` is formed by extending a side of a triangle. The triangle has angles 94° and 90°, so the third angle is `180° - 94° - 90° = -4°`, which is impossible. I must have misinterpreted the diagram. Let's assume it's a simple reflex angle. Given the complexity, I'll calculate based on the surrounding angles. The angle `p°` is likely 266° (360° - 94°).

Diagram 9: Trapezoid or Irregular Quadrilateral

- q°: The sum of angles in a quadrilateral is 360°. We have three angles: 57°, 90° (right angle), and 90° (another right angle).
- Calculation: `q° = 360° - 57° - 90° - 90° = 123°`

Diagram 10: Star-like Shape

- r°: The shape is composed of two triangles sharing a side. The sum of angles in a triangle is 180°. For the lower triangle, we have 39° and 85°.
- Calculation: The third angle in the lower triangle is `180° - 39° - 85° = 56°`. This angle is vertically opposite to an angle in the upper triangle. The upper triangle has angles `r°`, 56°, and another angle. Without more information, I'll assume the upper triangle is isosceles or use the fact that the sum of angles around a point is 360°. Given the complexity, I'll calculate `r°` as `180° - 56° - 56° = 68°` if it's isosceles.

Diagram 11: Parallel Lines with Transversal

- s°: The angles on a straight line add up to 180°. We have 122° and 147°, but these are not on the same line. The angle `s°` is formed by the intersection of lines. The angle adjacent to `s°` is 180° - 147° = 33°. The angle adjacent to `s°` on the other side is 180° - 122° = 58°. So, `s° = 360° - 33° - 58° - 180° = 89°`.

Diagram 12: Complex Angle with Multiple Lines

- t°: The sum of angles around a point is 360°. We have 264°, 26°, and `t°`.
- Calculation: `t° = 360° - 264° - 26° = 70°`

Final Answers:

- a° = 42°
- b° = 132°
- c° = 71°
- d° = 71°
- e° = 71°
- f° = 38°
- g° = 82°
- h° = 98°
- i° = 63°
- j° = 117°
- k° = 117°
- l° = 132°
- m° = 45°
- n° = 67°
- o° = 36°
- p° = 266° (assuming it's a reflex angle)
- q° = 123°
- r° = 68° (assuming isosceles triangle)
- s° = 89°
- t° = 70°

Note: Some calculations, particularly for `p°`, `r°`, and `s°`, involve assumptions due to the complexity of the diagrams. In a real classroom setting, additional context or clarification might be needed.