Angle sum

There are 360^\circ in a complete turn.

360° angle diagram

There are 180^\circ in half a turn (a straight line).

180° angle diagram
Question

Find the size of angle {z}:

360° angle sum diagram

There are 360^\circ in a complete turn, so z + 40 + 110 + 130 = 360

z + 280 = 360

z = 80 ^\circ

Question

What is the size of angle {p}?

180° angle sum diagram

The angles on a straight line add up to 180^\circ, so p + 140 = 180.

p = 40 ^\circ

Angles in a triangle

The angles in a triangle add up to 180^\circ.

Angles in a quadrilateral

The angles in a quadrilateral add up to 360^\circ.

This works for any quadrilateral.