9514 1404 393
Answer:
a = 108°
b = 24°
Explanation:
a) The pentagon will have interior angles of 540°/5 = 108°.
Angle a = 108°
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b) The reflex angle at a vertex of the pentagon is 360° -108° = 252°. At the obtuse angle of the unshaded triangle, 120° of that amount is take up by two internal angles of the equilateral triangles. Those are 60° each. So, the obtuse angle in the unshaded triangle is ...
252° -120° = 132°
That triangle is isosceles, so the angle at b is ...
2b° +132° = 180°
b = (180 -132)/2 = 48/2 = 24
Angle b = 24°