Question

b)
angle | reason
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Explanation:

Identify parallel lines and transversals

Using the Parallel Lines knowledge point, we identify two parallel horizontal lines indicated by the arrows. The left side of the large triangle acts as a transversal line cutting through both parallel lines.

Determine Angle 2

Using the Parallel Lines knowledge point, the angle labeled \(75^\circ\) and \(\angle 2\) are corresponding angles because they lie in the same relative position at each intersection. Therefore, we have:

$$ \angle 2 = 75^\circ $$

Determine Angle 1

Using the Straight Angle Theorem knowledge point, \(\angle 1\) and \(\angle 2\) lie on a straight line and are supplementary. Thus:

$$ \angle 1 + \angle 2 = 180^\circ $$

$$ \angle 1 + 75^\circ = 180^\circ \implies \angle 1 = 105^\circ $$

Determine Angle 3

Using the Parallel Lines knowledge point, the right side of the triangle acts as another transversal. The angle labeled \(42^\circ\) and \(\angle 3\) are corresponding angles. Therefore:

$$ \angle 3 = 42^\circ $$

Answer:

Angle	Reason
\(\angle 2 = 75^\circ\)	Corresponding angles are equal
\(\angle 3 = 42^\circ\)	Corresponding angles are equal