SECTION B - STRAIGHT LINE GEOMETRY; APPLICATION Question 2 -

The diagram shows two angles, $x$ and $40^\circ$, that lie on a straight line. Angles on a straight line sum to $180^\circ$.

$$x + 40^\circ = 180^\circ$$

Reason 2.1.1: Angles on a straight line.

The diagram shows four angles, $a, b, c, d$, around a central point where two lines intersect. The sum of angles around a point is $360^\circ$.

$$a + b + c + d = 360^\circ$$

Reason 2.1.2: Angles around a point (or angles in a revolution).

The diagram shows two parallel lines, PQ and RS, intersected by a transversal. Angles $e$ and $f$ are interior angles on the same side of the transversal. These are also known as co-interior angles. Co-interior angles between parallel lines are supplementary (add up to $180^\circ$).

$$e + f = 180^\circ$$

Reason 2.1.3: Co-interior angles are supplementary (PQ || RS).

The diagram shows two parallel lines, PQ and RS, intersected by a transversal. Angles $e$ and $g$ are alternate interior angles. Alternate interior angles between parallel lines are equal.

$$e = g$$

Reason 2.1.4: Alternate interior angles are equal (PQ || RS).

The diagram shows two parallel lines, RS and TU, intersected by a transversal. Angles $i$ and $g$ are corresponding angles. Corresponding angles between parallel lines are equal.

$$i = g$$

Reason 2.1.5: Corresponding angles are equal (RS || TU).