Question

In the figure below, each side of hexagon MNPQRS is 2 cm, and each angle measures 120°.

An illustration of a hexagon M N P Q R S. Three lines S N, N Q, and Q S are drawn to form a triangle inside the hexagon.


If triangle NQS is an equilateral triangle, with each side 3.5 cm long, what is m
∠
MNS?
A.
45°
B.
60°
C.
30°
D.
25°

Answer 1

B. 60°. To find the measure of angle MNS, we first determine the measure of angle NSM, which is 120 degrees. The sum of the angles in triangle MNS is 180 degrees, so angle MNS is 60 degrees.

Step-by-step explanation:

To find the measure of angle MNS, we need to first determine the measure of angle NSM. Since triangle NQS is an equilateral triangle, each of its angles measures 60 degrees. Since angle NSM is an exterior angle of triangle NQS, it is equal to the sum of the two remote interior angles, which are both 60 degrees. Therefore, angle NSM is equal to 120 degrees.

Next, we can use the fact that the sum of the angles in any hexagon is 720 degrees. Since each angle in hexagon MNPQRS measures 120 degrees, the sum of the angles in triangle MNS is 180 degrees (720 - 2*120).

Therefore, angle MNS is equal to 180 - 120 = 60 degrees. So the correct answer is B. 60°.

Answer 2

C - 30°

Step-by-step explanation:

angle MNS and angle MSN are both the same, since they are next to a equilateral triangle, all the isosceles triangles will be the same as well