Everything Maths Grade 10

Worked example 1: Finding angles

QUESTION

Find all the unknown angles. IsEF∥CG? Explain your answer.

A C G

䈀

䐀

䘀

䔀

x s

y

p

r

60 ◦

160 ◦

SOLUTION

Step 1: Use the properties of parallel lines to find all equal angles on the diagram

Redraw the diagram and mark all the equal angles.

A C G

䈀 䐀 䘀 䔀 x s

y

p

r

60 ◦

160 ◦

Step 2: Determine the unknown angles

AB ∥CD (given)

)x^ = 60° (alt\s;AB∥CD)

y^+ 160° = 180° (co-int\s;AB∥CD)

)y^ = 20°

^p = ^y (vert opp\s=)

)^p = 20°

^r = 160° (corresp\s;AB∥CD)

s^+ ^x+ 90° = 180° (\s on a str line)

^s+ 60° = 90°

)^s ; = 30°

Step 3: Determine whetherEF∥CG

IfEF ∥CGthenp^will be equal to corresponding angles^, butp^= 20°ands^= 30°. ThereforeEFis not
parallel toCG.

Exercise 7 – 1:

1.Use adjacent, corresponding, co-interior and alternate angles to fill in all the angles labelled with letters

in the diagram:

Chapter 7. Euclidean geometry 239