\(\triangle ABC\) 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 \(ADEC?\)

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

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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?

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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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