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