Example 15 A rectangular swimming pool measures 20 m by 16 m.
A path of uniform width of x em is built around the pool.
If the area of the path is 100 m square, find the width of the path, giving your answer correct to 3 significant
figures

Here's a link to the

https://cutt.ly/kzjInUL

The total figure width should be 54 m total

Refer to the figure shown below.

Let x =  measure of the second angle.

The measure of the third angle is 57° more than 1/2 the measure of the second angle. Therefore the measure of the third angle is x/2 + 57°.

The sum of the angles in a triangle is 180°. Therefore

66 + x + (x/2 + 57) = 180
(3/2)x + 123 = 180
(3/2)x = 57
x = (2/3)*57 = 38°

The measure of the second angle is 38°