Question

Here is a pentagon. The pentagon has one line of symmetry. Work out the size of the angle marked x.

a) 60 degrees
b) 90 degrees
c) 120 degrees
d) 150 degrees

Answer 1

The size of the angle marked x in the pentagon is 36 degrees.

Step-by-step explanation:

The pentagon has one line of symmetry, which means that if you fold the shape along that line, the two halves will match up perfectly. In a regular pentagon, all the angles are equal, so we can divide the total sum of the interior angles by 5 to find the size of each angle. The sum of the interior angles of a pentagon is 540 degrees, so each angle in a regular pentagon is 540 / 5 = 108 degrees. However, in this case, we are given that one of the angles is marked as x. Since the pentagon has only one line of symmetry, the angle marked x must be half of the difference between 180 degrees and 108 degrees. So, x = (180 - 108) / 2 = 36 degrees.