Skywalker18 wrote:

In the figure, JKLMNP is a regular hexagon .Find the measure of \(\angle\) MQN.

A. \(30^{\circ}\)

B. \(45^{\circ}\)

C. \(50^{\circ}\)

D. \(60^{\circ}\)

E. \(75^{\circ}\)

vinnisatija Theres a very simple explanation for this question.

Remember the formula for the sum of internal angles of a polygon.

Sum of angles= 180 X (n-2) ; where n= number of sides

In our case ; 180 ( 6-2) = 720.

Now this is a regular hexagon. All the angles are equal and all the sides are also equal.

therefore Each angle = 120

Now consider triangle LMN

we know angle M=120.

Since all the sides are equal, we know this is an isosceles triangle.

2x+120=180

x=30.

So angle L= N= 30.

Similarly, in triangle KLM,

angle k and M = 30.

From what we have proved above,

Angle QMN 120-30 = 90

Now we have angle QMN+ Angle MQN + angle QNM = 180

90+MQN+30=180

MQN=60

Hope its clear. Let me know through the kudos button