Question

One side of each pentagon lies along a side of the octagon.

AB is a side of the octagon.
AC is a side of one of the pentagons.
BC is a side of the other pentagon.
Work out the size of angle y.
Show your working clearly.

Answer 1

The size of angle y is 126°

Explanation:

From the diagram of the regular polygons, we have;

One side of each pentagon lies along a side of the octagon

The interior angle of the octagon > The interior angle of the pentagon

Each interior angle of a regular pentagon = 108°

Each interior angle of a regular octagon = 135°

Therefore, ∠ABC = 135° - 108° = 27°

Similarly, ∠BAC = 135° - 108° = 27°

Therefore, by triangle the angle sum theorem, we have;

∠y = ∠ACB = 180° - ∠BAC - ∠ABC = 180° - 27° - 27° = 126°

The size of angle y, ∠y = 126°.