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
[tex]a=b=c=d=e=f[/tex]
The sum of all the angles is equal to 360°. Therefore, each angle will be equal to
[tex]\begin{gathered} a=\frac{360}{6} \\ a=60^{\circ} \end{gathered}[/tex]
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,
[tex]\begin{gathered} 60+2\theta=180\text{ (Sum of angles in a triangle)} \\ 2\theta=180-60=120 \\ \therefore \\ \theta=60\degree \end{gathered}[/tex]
From this, we can get the smaller triangle ZCY and find the angle ZCY as follows:
Therefore, angle ZCY can be calculated as
[tex]\begin{gathered} x+60+90=180\text{ (Sum of angles in a triangle)} \\ x=180-60-90 \\ x=30\degree \end{gathered}[/tex]
Therefore, the value of angle ZCY is 30°.
