Lines and Angles Worksheets - Printable Angles and Parallel Lines ... - Free Printable

I will solve the problem by calculating all the missing angles labeled from a° to t° on the worksheet. I'll go through each shape systematically, using geometric principles like the sum of angles in a triangle (180°), quadrilateral (360°), and properties of parallel lines and transversals.

Let's start with the first shape, which is a right-angled triangle.

Shape 1: Right-Angled Triangle

- We are given one angle as 48°.
- The symbol for a right angle indicates another angle is 90°.
- The sum of angles in any triangle is 180°.
- Therefore, `a° = 180° - 90° - 48° = 42°`.

Shape 2: Parallelogram

- In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°).
- We are given one angle as 74°.
- The opposite angle `f°` must also be 74°.
- The adjacent angles `j°` and `k°` must each be `180° - 74° = 106°`.

Shape 3: Isosceles Triangle between Parallel Lines

- This is an isosceles triangle with two base angles marked as 72°.
- The third angle `c°` is `180° - 72° - 72° = 36°`.
- Since the triangle sits between two parallel lines, the angle `d°` is vertically opposite to `c°`, so `d° = 36°`.
- The angle `e°` is an alternate interior angle to one of the 72° base angles, so `e° = 72°`.

Shape 4: Triangle with an Exterior Angle

- The exterior angle is given as 126°.
- The exterior angle is equal to the sum of the two opposite interior angles.
- One interior angle is 59°.
- So, `g° = 126° - 59° = 67°`.
- The third angle `h°` is `180° - 59° - 67° = 54°`.

Shape 5: Right-Angled Triangle

- Given one angle is 38° and it's a right triangle (90°).
- So, `i° = 180° - 90° - 38° = 52°`.

Shape 6: Quadrilateral (Trapezoid)

- We are given three angles: 88°, 90°, and 68°.
- The sum of angles in a quadrilateral is 360°.
- So, `m° = 360° - 88° - 90° - 68° = 114°`.
- The angle `n°` is vertically opposite to the 88° angle, so `n° = 88°`.

Shape 7: Triangle with an Exterior Angle

- The exterior angle is 112°.
- One interior angle is 57°.
- So, `o° = 112° - 57° = 55°`.

Shape 8: Irregular Pentagon

- The sum of interior angles of a pentagon is `(5-2) * 180° = 540°`.
- We are given three angles: 94°, 90°, and 90°.
- The other two angles are both `p°`.
- So, `94° + 90° + 90° + p° + p° = 540°`.
- `274° + 2p° = 540°`.
- `2p° = 266°`.
- `p° = 133°`.

Shape 9: Right-Angled Triangle

- Given one angle is 41° and it's a right triangle (90°).
- So, `q° = 180° - 90° - 41° = 49°`.

Shape 10: Triangle with an Exterior Angle

- The exterior angle is 85°.
- One interior angle is 36°.
- So, `r° = 85° - 36° = 49°`.

Shape 11: Angles on a Straight Line

- Angles on a straight line sum to 180°.
- We have angles 122° and `s°`.
- So, `s° = 180° - 122° = 58°`.

Shape 12: Angles around a Point

- Angles around a point sum to 360°.
- We are given one angle as 264°.
- The other angle is `t°`.
- So, `t° = 360° - 264° = 96°`.

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Here is the complete list of answers:

- a° = 42°
- c° = 36°
- d° = 36°
- e° = 72°
- f° = 74°
- g° = 67°
- h° = 54°
- i° = 52°
- j° = 106°
- k° = 106°
- m° = 114°
- n° = 88°
- o° = 55°
- p° = 133°
- q° = 49°
- r° = 49°
- s° = 58°
- t° = 96°

All missing angles have been calculated based on standard geometric rules.