Find the Size of Angle $a$ with Parallel Lines and Transversal, Justify Your Answer

Question

(i) Write down the size of the angle marked $a$. (ii) Give a reason for your answer. (Note: The diagram shows an angle formed by a transversal intersecting two parallel lines, with angle $a$ corresponding to a known angle above it, which is implied to be equal due to parallel line rules.)

Accepted Answer

(i) The size of angle $a$ is equal to the corresponding angle above it (typically 45°/90°/180° based on standard parallel line diagrams; assuming a common corresponding angle, 45° is a common example, but the exact value depends on the full diagram, the reasoning is corresponding angles are equal). (ii) Corresponding angles are equal when a transversal cuts two parallel lines.

Answer

Step 1: Identify that the diagram shows two parallel lines cut by a transversal, creating corresponding angles. Step 2: Recognize that angle $a$ is a corresponding angle to the given angle at the top of the diagram. Step 3: Apply the corresponding angles postulate: when two parallel lines are intersected by a transversal, corresponding angles are congruent (equal in measure). Step 4: State the measure of angle $a$ as equal to the matching corresponding angle, and provide the corresponding angles rule as the reason.