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Angle facts
- Angles on a straight line add to 180 °.
- Angles around a point add to 360 °. Whenever possible show your working by writing an equation and solving it.
- When straight lines cross, the “vertically opposite” angles are equal:
- When a straight line cuts a pair of parallel lines: (a) all the acute angles are equal (b) all the obtuse angles are equal
Names for pairs of angles:
x
x
x + 100 + 60 + 90 = 360 °
x 40 180
40 x^ ^180 ^40 ^140
x 250 360
x 360 250 110 100
x x
Alternate (Z) angles are equal
Corresponding (F) angles are equal
Angle is the acute or obtuse (not reflex) angle between lines AB and BC.
A
B
C
A B
C
Angles in a triangle The angles in a triangle add to 180°. Given two angles, we can find the third
Each exterior angle is the sum of the opposite two interior angles
If the triangle is isosceles (look for tick marks), if I know one angle I can
find both the others
Supplementary angles add to 180
x x
y
2 x 110 180 2 x 180 110 70 x 35
y 40 40 180 y 180 80 100
a
b 180 (^) a b
a b
45
100 x
x 45 100 180 x 180 145 35
If it is a regular polygon, each interior angle will be ^
180 n 2 n
(One can more easily get the same result using 180° - exterior angle).
Tangents to a circle
.
axis of symmetry
Atangent is perpendicular (at 90°) to the radius that meets it.
Tangents are equal length, to the point where they intersect o hence triangle ABC is isosceles.
Line OB is an axis of symmetry, so: o line AC cuts it at 90° o triangles OBC and OBA are mirror images of each other.
Triangle OAC is isosceles because OA and OC are equal length (= radius).
A
B
C
90
90
O
