What this guide covers
Selected Sec 2 G1 skills: special quadrilateral and regular-polygon angle reasoning. Circle properties and longer upper-secondary angle chains are separate topics.
Two useful sums
Any quadrilateral's interior angles sum to 360°. One exterior angle at each vertex of a convex polygon sums to 360°; divide by the number of sides only when those exterior angles are equal.
Use regularity correctly
Find one exterior angle, one interior angle and the interior-angle sum of a regular decagon.
- Ten equal exterior angles total 360°, so each is 360°÷10=36°.
- Each interior angle is 180°−36°=144°.
- The interior-angle sum is (10−2)×180°=1440°.
Check: Ten equal interior angles of 144° also total 1440°.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
Three angles in a quadrilateral are 80°, 95° and 110°. Find the fourth and state the reason.
A quadrilateral's interior angles total 360°, so the fourth is 360°−80°−95°−110°=75°. No regularity is needed.
Find one exterior and one interior angle of a regular hexagon.
One exterior angle is 360°÷6=60°. Its adjacent interior angle is 180°−60°=120°. Regularity justifies equal exterior angles.
Where this connects
- Earlier: line and triangle reasons →
Straight-line and triangle facts support longer geometry.
- Later: combined angle deductions →
The Upper Secondary challenge uses several reasons in one figure.
Sources and scope
Original Mentora angle questions aligned to selected Sec 2 G1 scope in the MOE G2/G3 Mathematics syllabus. No school-paper diagram or question was reused.