Question

Solve for the measure of angle ZCY in the regular hexagon .

Answer 1

The diagram provided is a regular hexagon. This means that all the sides and angles are equal.

We can divide the hexagon into 6 parts by drawing diagonals as follows:

For a regular hexagon, all the labelled angles are equal, such that

`a=b=c=d=e=f`

The sum of all the angles is equal to 360°. Therefore, each angle will be equal to

`\begin{gathered} a=(360)/(6) \\ a=60^(\circ) \end{gathered}`

This means that angle ZCX is equal to 60°.

Hence, we can bring out Triangle XCZ from the question:

The base angles are equal since the vertical sides are equal.

Therefore,

`\begin{gathered} 60+2\theta=180\text{ (Sum of angles in a triangle)} \\ 2\theta=180-60=120 \\ \therefore \\ \theta=60\degree \end{gathered}`

From this, we can get the smaller triangle ZCY and find the angle ZCY as follows:

Therefore, angle ZCY can be calculated as

`\begin{gathered} x+60+90=180\text{ (Sum of angles in a triangle)} \\ x=180-60-90 \\ x=30\degree \end{gathered}`

Therefore, the value of angle ZCY is 30°.