Triad of Triangles
As shown in the diagram above, there lie 3 equilateral triangles between 2 parallel lines, such that they do not overlap each other but share part of each other's side.
Find the measure of in degrees.
Note: The diagram is not necessarily drawn to scale.
The answer is 100.
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1 solution
Relevant wiki: Complementary and Supplementary Angles
Since the angles of the triangles are all 6 0 ∘ , and their adjacent parallel bases are collinear, then their relative sides are parallel, which transforms the unaligned-triangle diagram into the new diagram as shown above. No matter the lengths of all three equilateral triangle, the result of x is the same.
Thus, since the angles formed by two black lines are supplementary, x = 1 8 0 ∘ − 8 0 ∘ = 1 0 0 ∘ .