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Derive angle sums and use triangle, quadrilateral and regular-polygon properties to solve problems.
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Connect & Check
Polygon: closed straight-sided shape. Regular: all sides and angles equal. Interior: inside angle. Exterior: turn between a side and the extension of the previous side. Isosceles: two equal sides.
Intentional practice feedback after your attempt
115°.
Straight-line sum.
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x=70.
Balanced operations.
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45.
Eight equal turns.
Present
A triangle has angle sum 180°, proved using a parallel through a vertex. A convex n-gon splits from one vertex into n−2 triangles, giving (n−2)×180°. Walking once round a convex polygon turns 360°. In a regular polygon each exterior angle is 360÷n and the interior is 180 minus that turn.
Decide whether an angle sum or a single regular angle is needed. Use equal sides to identify equal opposite angles. Check regularity before dividing a sum by n.
Optional scaffold
Start with 180°.
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y=65°.
180−38−77.
Optional scaffold
The other two angles are equal.
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Base angles 62° each.
(180−56)÷2.
Optional scaffold
Count triangles, not sides.
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900°.
(7−2)×180.
Optional scaffold
One full turn is shared equally.
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36° exterior; 144° interior.
360÷10; 180−36.
Apply
Optional scaffold
Draw diagonals from one vertex.
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360°, 540°, 720°; add 180° for one extra triangle.
Use n−2.
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15 sides; 156°.
360÷24=15; 180−24.
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112°, 68°, 112°.
Opposite angles equal; adjacent angles supplementary.
Optional check after A2: 15×24=360. Angle sums are exact; do not round the number of sides.
Apply and extend
Intentional practice feedback after your attempt
A rhombus with angles 60°,120°,60°,120° has equal sides but is not a square.
Square also requires right angles.
Intentional practice feedback after your attempt
No; 360÷50=7.2 is not a whole number of sides.
Regular exterior angles must complete a turn.
Access, Scaffold, Core and Stretch support the same goal. Stretch deepens reasoning for either qualification tier.
Recall & Review
Retrieval without notes
Six retrieval points. Enter a number, decimal, fraction such as 3/2, or mixed number such as 1 1/2. Equivalent numeric values are accepted. Unsupported notation goes to teacher review. For rounding, also communicate the requested accuracy in written work; numerical scoring cannot judge significant trailing zeros.
Not checked.
Independent exit evidence
P1–P2: five minutes, no notes, 4 marks. Your teacher reviews working and explanations. Full assessment solutions are not embedded.
Recall & Review and prepare
Congruent figures have the same shape and size. Corresponding sides and angles match even when one figure is rotated or reflected. Triangle congruence needs sufficient measurements.
Retrieve F1 again in one week. Bring your working and one question.
Your progress summary
Completion records attempts, not mastery. Retrieval points describe the latest checked attempt. Your teacher reviews P1–P2 separately and checks retained understanding after a delay.
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Optional extension activities
Allow 10–15 minutes if the main practice is secure. Show your method, explain a check and justify your conclusion.
Stretch
Reveal a worked check after attempting
Exterior angle=360/15=24°, interior=156°.
Deep challenge
Reveal a worked check after attempting
Exterior=15°, sides=360/15=24.