16 Angles of a Triangle
By studying this lesson you will be able to;
² solve simple problems using the theorem “The sum of the interior angles of a
o
triangle is 180 ”,
² solve simple problems using the theorem “The exterior angle of a triangle is
equal to the sum of the interior opposite angles”.
Let us recall several results in geometry that you have learnt earlier related to
straight lines.
² A pair of adjacent angles on a straight line are supplementary. P
a b
A B
O
AOB is a straight line.
∴ a + b = 180o.
a
² The sum of the angles around a point is 360o. d b
c
a + b + c + d = 360o
² The vertically opposite angles formed by the intersection of two straight lines
are equal.
A C
O
D B
>
>
>
>
AB and CD are straight lines. AOC = BOD and AOD = COB '
83
for free distribution.
, ² Angles related to parallel lines
A
Q
a
d c b
C B
n k l
m
P
D
AB CD'
² c = k and d = l (alternate angles)
² a = k, b = l, d = n, c = m (corresponding angles)
² d + k = 180o and c + l = 180o (allied angles)
In the lesson on triangles and quadrilaterals learnt in grade 8, we identified that;
² the sum of the interior angles of a triangle is 180o and the sum of the interior
angles of a quadrilateral is also 360o.
a
q
p
s
b c r
a + b + c = 180o p + q + r + s = 360o
² the sum of the exterior angles of a triangle is 180o and the sum of the exterior
angles of a quadrilateral is also 360o.
a q
r
p
c s
b
a + b + c = 360o p + q + r + s = 360o
84
for free distribution.
By studying this lesson you will be able to;
² solve simple problems using the theorem “The sum of the interior angles of a
o
triangle is 180 ”,
² solve simple problems using the theorem “The exterior angle of a triangle is
equal to the sum of the interior opposite angles”.
Let us recall several results in geometry that you have learnt earlier related to
straight lines.
² A pair of adjacent angles on a straight line are supplementary. P
a b
A B
O
AOB is a straight line.
∴ a + b = 180o.
a
² The sum of the angles around a point is 360o. d b
c
a + b + c + d = 360o
² The vertically opposite angles formed by the intersection of two straight lines
are equal.
A C
O
D B
>
>
>
>
AB and CD are straight lines. AOC = BOD and AOD = COB '
83
for free distribution.
, ² Angles related to parallel lines
A
Q
a
d c b
C B
n k l
m
P
D
AB CD'
² c = k and d = l (alternate angles)
² a = k, b = l, d = n, c = m (corresponding angles)
² d + k = 180o and c + l = 180o (allied angles)
In the lesson on triangles and quadrilaterals learnt in grade 8, we identified that;
² the sum of the interior angles of a triangle is 180o and the sum of the interior
angles of a quadrilateral is also 360o.
a
q
p
s
b c r
a + b + c = 180o p + q + r + s = 360o
² the sum of the exterior angles of a triangle is 180o and the sum of the exterior
angles of a quadrilateral is also 360o.
a q
r
p
c s
b
a + b + c = 360o p + q + r + s = 360o
84
for free distribution.
