91Ó°ÊÓ

Find the measure of each acute interior angle of a regular octagram.

\(\angle X^{\prime} Y Z^{\prime}\) is the image of \(\angle X Y Z\) following a \(100^{\circ}\) counterclockwise rotation of \(\angle X Y Z\) about point \(Y\). If \(\mathrm{m} \angle X Y Z=\frac{5 x}{6}\) and \(\mathrm{m} \angle X^{\prime} Y Z^{\prime}=130^{\circ},\) find \(x\)

Consider any regular polygon; find and join (in order) the midpoints of the sides. What does intuition tell you about the resulting polygon?

Consider a regular hexagon \(R S T U V W\). What does intuition tell you about \(\triangle R T V\), the result of drawing diagonals \(\overline{R T}, \overline{T V},\) and \(\overline{V R} ?\)

Given:\(\quad\) A line \(m\) and a point \(T\) not on \(m\)Suppose that you do the following: i) Construct a perpendicular line \(r\) from \(T\) to line \(m\) ii) Construct a line \(s\) perpendicular to line \(r\) at point \(T\) What is the relationship between lines \(s\) and \(m ?\)

The face of a clock has the shape of a regular polygon with 12 sides. What is the measure of the angle formed by two consecutive sides?

The top surface of a picnic table is in the shape of a regular hexagon. What is the measure of the angle formed by two consecutive sides?

For the concave quadrilateral \(A B C D\) explain why the sum of the interior angles is \(360^{\circ}\) (HINT: Draw \(\overline{B D}\) )

Is it possible for a polygon to have the following sum of measures for its interior angles? a) \(600^{\circ}\) b) \(720^{\circ}\)

Is it possible for a regular polygon to have the following measures for each interior angle? a) \(96^{\circ}\) b) \(140^{\circ}\)