Angles between Lines and Triangles – Worked Examples

Example 10.2.1:

Find the value of the lettered angles.

Solution:

Check if you have parallel lines. There are parallel lines so let’s apply angles in parallel lines.

But, let’s solve the angles in the triangle first

from the diagram;

b = c   (base angle of isosceles triangle)

⇒ 58° + b + c = 180° (sum of angles in a Δ)

58° + c° + c°  = 180° (since b = c)

58° + 2c° = 180°

2c° = 180° – 58°

2c° = 122°

Divide both sides by 2

c = \( \frac{122}{2} \ \scriptsize = 61^o \)

∴ b = c = 61°

e = c = 61^° (alternate angles)

a = 58° + e (alternate angles)

a = 58° + 61°

a = 61° + 58°

a = 119°

f = b (alternate angles)

f = 61°

d = 58° + f (alternate angles)

= 58° + 61°

= 119°

Example 10.2.2:

Find the value of x

Solution

x + 30° + 40° = 90° (complementary angles)

x + 70° = 90°

x = 90° – 70°

x = 20°