Geometry

# Regular Polygons - Problem Solving

$$\triangle ABC$$ is a regular triangle with side length $$6.$$ If a triangle $$\triangle BDE$$ is cut from $$\triangle ABC$$, where the length of $$\overline{DB}$$ and $$\overline{EB}$$ are both equal to $$1$$, what is the perimeter of remaining figure $$ADEC?$$

Which of the following facts about regular polygons is false?

$$ABCD$$ is a square. The point $$E$$ is located within $$ABCD$$, such that $$ABE$$ is an equilateral triangle. What is the measure (in degrees) of $$\color{red} {\angle \text{CBE} }$$?

Consider a polygon with $$n$$ vertices such that all internal angles are obtuse. If the sum of $$n-1$$ angles in this polygon is $$973^{\circ},$$ what is the last angle in degrees?

A regular polygon has interior angles of $$150^\circ$$. $$A, B, C, D$$ are 4 consecutive points of this polygon. What is the measure (in degrees) of $$\angle ADC?$$

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