 |
 |
 |
|
 |
|
 |
|
 |
|
 |
|
 |
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
|
Contents
Angle Properties of straight lines
Angle Properties of Parallel Lines
|
Angles Properties of Straight Lines
Activity 1
(a) Measure the two angles.
(b) Do
they add up to 180°?
(c) Do
you agree that adjacent angles on a straight line adds up to 180°?
Activity
2
 Draw any
two lines to intersect at T as shown. In the figure, â and ê are vertically
opposite angles. So are ĉ and ĝ.(a) Are
â and ê equal?
(b) Are ĉ
and ĝ also equal?
(c) What
can you say about vertically opposite angles?
Activity
3
 Draw a
similar figure similar as the one on the right. Notice that they all have the
same vertex O. These angles are known as angles at a point.(a) Do
they add up to 360°?
(b)
Notice that they have the same vertex O?
The
above activities prove that
The sum
of the adjacent angles on a straight line is 180°. (adj Ðs
on a str. l)
Vertically
opposite angles are equal (vert. opp. Ðs)
Sum of
angles at a point equals to 360° ( Ðs
at a point)
Example
1
 
AOB and
COD are straight lines. Find the values of x, y and z.
65° =
40° + x° (vert. opp. s)
x = 25
y° +
40° = 90°
y = 50
65° + z° +
y° = 180° (adj. s on str. l)
65° + z° + 50° = 180°
z =
65
Example
2
AB and
CD are straight lines. Form an equation in x and solve the equation.
2x° +
15° = x° + 85° (vert. opp. s)x = 70
|
n
the figure, ACB is as straight line. â and
Ð
b are adjacent angles. Thus, we
call them adjacent angles on a straight line. Draw a similar figure similar to
the one on the right.
