Answer: x = 30
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Step-by-step explanation:
If a regular polygon has n sides, then each interior angle has the measure of
i = 180(n-2)/n
In this case, we have n = 6 sides, so,
i = 180(n-2)/n
i = 180(6-2)/6
i = 120
Each interior angle of a regular hexagon is 120 degrees.
This means the bottom-right angle of the triangle is 120 degrees. The upper-right angle of that triangle is shown to be x degrees. The remaining angle is also x due to the triangle being isosceles (recall that regular hexagons have all sides the same length). Isosceles triangles have congruent base angles, which are opposite the congruent sides.
Use the fact that for any triangle, the three angles always add to 180, and we get...
x+120+x = 180
2x+120 = 180
2x = 180-120
2x = 60
x = 60/2
x = 30