Question

In the figure below, each side of hexagon MNPQRS is 2 cm, and each angle measures 120°.If triangle NQS is an equilateral triangle, with each side 3.5 cm long, what is m/MNS?OA. 45°OB. 25°OC. 30°OD. 60°

Answer 1

To find:

THe value of measure of angle MNS.

Solution:

Given that each angle of hexagon is 120 degrees.

It is known that the sum of interior angles of a triangle is 180 degrees. Here, the measure of angle SMN is 120 degrees. Since, SM = MN, so, angle MNS and angle NSM are equal. SO,

`\begin{gathered} \angle MNS+\angle NSM+\angle SMN=180 \\ 2\angle MNS+120=180 \\ 2\angle MNS=60 \\ \angle MNS=30 \end{gathered}`

Thus, the option C is correct.