Answer:
a = 80°
Step-by-step explanation:
In order to solve this figure, we need to find a useful relationship between the various angles. We can use the straight angle at the upper left vertex of the equilateral triangle.
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The sum of angles there is ...
a + 60° +(a/2) = 180°
3/2a = 120° . . . . . . . . . . subtract 60°, collect terms
a = 80° . . . . . . . . multiply by 2/3
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Additional comment
All triangles are isosceles, because they all have 2 (or more) sides the same length. That means the base angles are half the supplement of the a.pex angle. Of course, adjacent vertices of a rhombus have supplementary angles.
