Try some yourself
Question 1
Find the unknown angles in each of these diagrams, which represent part of the bracing structure supporting a marquee.
Answer
(a) In ΔABC,
therefore
(b) In ΔFGH,
therefore
As EFG is a straight line,
So
In ΔEFH,
Question 2
Deduce the value of α in the triangle below.
Answer
Lines XY and XZ are of equal length. This means that the triangle is isosceles, so the base angles 
and 
are equal. Then 
The third angle in the triangle is a right angle: 
.
Because the three angles in a triangle must add up to 180°,
Hence
Question 3
Find the unknown angles in the following isosceles triangles, which represent roof rafters.
Answer
(a) As this is an isosceles triangle, α = β.
So
Therefore
(b) As this is an isosceles triangle, γ = δ.
So
Therefore
