gcse maths revision | geometry and measure
angles in parallel lines - worksheet

skill
group a - types of angles in parallel lines
using the diagram below, state whether the pair of letters are alternate interior/exterior, co-interior, or corresponding to each other.

1) a and e are ...
2) b and f are ...
3) c and f are ...
4) c and g are ...
5) d and f are ...
6) d and h are ...
7) a and h are ...
8) b and g are ...
9) c and e are ...

group b - calculate missing angles
calculate the size of angle $\theta$. state any angle facts that you use for each question.

1)
2)
3)
4)
5)
6)

Question

gcse maths revision | geometry and measure
angles in parallel lines - worksheet

skill
group a - types of angles in parallel lines
using the diagram below, state whether the pair of letters are alternate interior/exterior, co-interior, or corresponding to each other.

1) a and e are ...
2) b and f are ...
3) c and f are ...
4) c and g are ...
5) d and f are ...
6) d and h are ...
7) a and h are ...
8) b and g are ...
9) c and e are ...

group b - calculate missing angles
calculate the size of angle $\theta$. state any angle facts that you use for each question.

1)
2)
3)
4)
5)
6)

Accepted Answer

{ "quality": "clear", "question_count": 15, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Parallel Line Angles", "Transversal Lines", "Angle Relationships" ], "current_concepts": [ "Parallel Line Angles", "Transversal Lines", "Angle Relationships" ] } ## Identify angle relationships in Group A We analyze the positions of each pair of angles relative to the parallel lines and the transversal line: - **Corresponding angles** lie in the same relative position at each intersection (e.g., top-left, bottom-right). - **Alternate interior angles** lie between the parallel lines on opposite sides of the transversal. - **Alternate exterior angles** lie outside the parallel lines on opposite sides of the transversal. - **Co-interior angles** (consecutive interior) lie between the parallel lines on the same side of the transversal. Let's classify each pair: 1) $a$ and $e$: Both are in the bottom-left position of their respective intersections. They are **corresponding** angles. 2) $b$ and $f$: Both are in the bottom-right position of their respective intersections. They are **corresponding** angles. 3) $c$ and $f$: Both are inside the parallel lines on opposite sides of the transversal. They are **alternate interior** angles. 4) $c$ and $g$: Both are in the top-left position of their respective intersections. They are **corresponding** angles. 5) $d$ and $f$: Both are inside the parallel lines on the same side of the transversal. They are **co-interior** angles. 6) $d$ and $h$: Both are in the top-right position of their respective intersections. They are **corresponding** angles. 7) $a$ and $h$: Both are outside the parallel lines on opposite sides of the transversal. They are **alternate exterior** angles. 8) $b$ and $g$: Both are outside the parallel lines on opposite sides of the transversal. They are **alternate exterior** angles. 9) $c$ and $e$: Both are inside the parallel lines on the same side of the transversal. They are **co-interior** angles. ## Solve Group B, Question 1 - **Given**: An angle of $44^\circ$ and an angle $\theta$. - **Analysis**: The angle $44^\circ$ and the angle vertically opposite to it are equal. The interior angle on the same side as $\theta$ is $44^\circ$. Thus, $\theta$ and the $44^\circ$ angle are co-interior angles, which are supplementary. - **Calculation**: $$ \theta = 180^\circ - 44^\circ = 136^\circ $$ ## Solve Group B, Question 2 - **Given**: An angle of $95^\circ$ and an angle $\theta$. - **Analysis**: The angle vertically opposite to $95^\circ$ is $95^\circ$. This angle and $\theta$ are alternate interior angles, which are equal. - **Calculation**: $$ \theta = 95^\circ $$ ## Solve Group B, Question 3 - **Given**: An angle of $72^\circ$ and an angle $\theta$. - **Analysis**: The two lines with arrows are parallel. The transversal line intersects them. The angle $\theta$ and the angle $72^\circ$ are corresponding angles, which are equal. - **Calculation**: $$ \theta = 72^\circ $$ ## Solve Group B, Question 4 - **Given**: An angle of $102^\circ$ and an angle $\theta$. - **Analysis**: The two lines with arrows are parallel. The angle alternate to $102^\circ$ is inside, and $\theta$ is supplementary to the corresponding angle. Specifically, the angle corresponding to $102^\circ$ is supplementary to $\theta$ along a straight line. - **Calculation**: $$ \theta = 180^\circ - 102^\circ = 78^\circ $$ ## Solve Group B, Question 5 - **Given**: A triangle with parallel lines. An angle of $7^\circ$, an angle of $111^\circ$, and $\theta$. - **Analysis**: The alternate interior angle to $7^\circ$ is part of the angle at the bottom. The interior angles of the triangle can be found using parallel line properties. The angle adjacent to $111^\circ$ on a straight line is $180^\circ - 111^\circ = 69^\circ$. Using the alternate interior angle property, the top angle of the smaller triangle is $7^\circ$. In the triangle containing $\theta$, the angles sum to $180^\circ$. - **Calculation**: $$ \theta = 111^\circ - 7^\circ = 104^\circ $$ Alternatively, using the exterior angle theorem where the exterior angle of a triangle is equal to the sum of the two opposite interior angles: $$ \theta + 7^\circ = 111^\circ \implies \theta = 104^\circ $$ ## Solve Group B, Question 6 - **Given**: A triangle with a parallel base. An interior angle of $23^\circ$ and an exterior angle $\theta$. - **Analysis**: The arrows indicate parallel lines. The alternate interior angle to $23^\circ$ is the adjacent angle at the top vertex. The angles on a straight line sum to $180^\circ$. - **Calculation**: Using the parallel line properties and triangle angle sum: $$ \theta = 180^\circ - 23^\circ = 157^\circ $$ ## Group A - Types of angles in parallel lines | No. | Problem | Answer | |---|---|---| | 1 | $a$ and $e$ are ... | corresponding | | 2 | $b$ and $f$ are ... | corresponding | | 3 | $c$ and $f$ are ... | alternate interior | | 4 | $c$ and $g$ are ... | corresponding | | 5 | $d$ and $f$ are ... | co-interior | | 6 | $d$ and $h$ are ... | corresponding | | 7 | $a$ and $h$ are ... | alternate exterior | | 8 | $b$ and $g$ are ... | alternate exterior | | 9 | $c$ and $e$ are ... | co-interior | ## Group B - Calculate missing angles | No. | Answer | |---|---| | 1 | $\theta = 136^\circ$ (Co-interior angles sum to $180^\circ$) | | 2 | $\theta = 95^\circ$ (Alternate interior angles are equal) | | 3 | $\theta = 72^\circ$ (Corresponding angles are equal) | | 4 | $\theta = 78^\circ$ (Co-interior angles sum to $180^\circ$) | | 5 | $\theta = 104^\circ$ (Exterior angle theorem / Alternate interior angles) | | 6 | $\theta = 157^\circ$ (Angles on a straight line / Alternate interior angles) | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Angles" ] }

No.	Answer
2	\(\theta = 95^\circ\) (Alternate interior angles are equal)
3	\(\theta = 72^\circ\) (Corresponding angles are equal)
4	\(\theta = 78^\circ\) (Co-interior angles sum to \(180^\circ\))
5	\(\theta = 104^\circ\) (Exterior angle theorem / Alternate interior angles)
6	\(\theta = 157^\circ\) (Angles on a straight line / Alternate interior angles)

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QUESTION IMAGE

Question

Explanation:

Identify angle relationships in Group A

Solve Group B, Question 1

Solve Group B, Question 2

Solve Group B, Question 3

Solve Group B, Question 4

Answer:

Group A - Types of angles in parallel lines

Group B - Calculate missing angles

No.	Problem	Answer
2	\(b\) and \(f\) are ...	corresponding
3	\(c\) and \(f\) are ...	alternate interior
4	\(c\) and \(g\) are ...	corresponding
5	\(d\) and \(f\) are ...	co-interior
6	\(d\) and \(h\) are ...	corresponding
7	\(a\) and \(h\) are ...	alternate exterior
8	\(b\) and \(g\) are ...	alternate exterior
9	\(c\) and \(e\) are ...	co-interior