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x + 135° = 180° Adjacent angles at intersecting lines
x = 180° – 135°
= 45°
y = 62° Vertically opposite angles

Self Practice 8.2b

1. In the following diagrams, PQ, RS and TU are straight lines. Find the values of x and y.
(a) S T (b) Q
P 140° T 32°
x y U
R 80° y Q R x 24° S
P
U

How do you solve problems? LEARNING
STANDARDS
11 T S Solve problems
U involving angles
In the diagram, POR and P x 60° y related to
TOQ are straight lines. Find y intersecting lines. CHAPTER
the values of x and y. O 72° R

Q 8
∠QOR and ∠TOR
∠POT = 72° ∠TOR + 72° = 180° are adjacent angles
x + 60° = 72° ∠POT and ∠QOR ∠TOR = 180° – 72° at intersecting lines.
x = 72° – 60° are vertically = 108°
opposite angles.
= 12° y + y = 108°
2y = 108°
y = 54°

Self Practice 8.2c

1. In the diagram, POR and QOT are 2. In the diagram, QOS and ROU are
straight lines. Find the values of x straight lines. OT is the bisector
and y. of ∠UOS. ∠POQ and ∠QOR are
complementary angles. Find the values
Q of x and y.
R
84°
O 38° U T
P 18° x y S P 40° x y S
U T Q O

R

187
Lines and Angles

08 TB Math F1.indd 187 11/10/16 12:17 PM