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Triangles, Quadrilaterals and Polygons
Properties of angles
Angles on a straight line
∠w + ∠x + ∠y + ∠z = 180º
(∠s on str. line)
y
x
w
z
Angles at a point
∠w + ∠x + ∠y + ∠z = 360º
(∠s at a pt.)
x
w
Vertically opposite angles
z
x
∠w = ∠y (vert. opp. ∠s)
y
w
∠x = ∠z (vert. opp. ∠s)
z
Corresponding angles
x
∠x = ∠y (corr. ∠s)
y
Alternate angles
x
∠x = ∠y (alt. ∠s)
y
Interior angles
∠x + ∠y = 180º (int. ∠s)
x
y
Adapted:
Integrated Mathematics GEOMETRY & MENSURATION
for Secondary 1
© Singapore Asia Publishers Pte Ltd. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE.
Look for other useful resources: www.sapgrp.com
y
Angle properties of triangles
Sum of angles in a triangle
y
∠x + ∠y + ∠z = 180º (sum of ∠s in ∆)
x
z
Exterior angles of a triangle
x
∠x + ∠y = ∠z (ext. ∠s of ∆)
z
Exterior angles of a Polygon
Sum of exterior angles of any polygon = 360º.
____
360º
For an n-sided regular polygon, each exterior angle = ​ n ​.
Interior angles of a Polygon
Sum of interior angles of any n-sided polygon = 180o × (n – 2).
180º × (n – 2)
____________
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For an n-sided regular polygon, each interior angle = ​ n ​. Adapted:
Integrated Mathematics GEOMETRY & MENSURATION
for Secondary 1
© Singapore Asia Publishers Pte Ltd. All rights reserved.
Reproducible for home/classroom use only.
STRICTLY NOT FOR SALE.
Look for other useful resources: www.sapgrp.com
y