91Ó°ÊÓ

WRITING A FORMUL. AVrite a formula to nd the number of sides \(n\) in a regular polygon given that the measure of one exterior angle is \(x^{\circ}\) .

REASONINGIn Exercises \(37-40,\) i nd the number of sides for the regular polygon described. Each interior angle has a measure of \(165^{\circ}\)

REASONINGIn Exercises \(37-40,\) i nd the number of sides for the regular polygon described. Each exterior angle has a measure of \(9^{\circ} .\)

PROVING A THEOREM Prove the Parallelogram Opposite Angles Converse (Theorem 7.8). (Hint: Let x ° represent m?A and m?C. Let y° represent m?B and m?D. Write and simplify an equation involving x and y. Given \(\angle A \cong \angle C, \angle B \cong \angle D\) Prove \(A B C D\) is a parallelogram.

Which of the following angle measures are possible interior angle measures of a regular polygon? Explain your reasoning. Select all that apply. $$ \begin{array}{llllllll} \mathrm{a} & 162^{\circ} & \mathrm{b} & 171^{\circ} & \mathrm{c} & 75^{\circ} & \mathrm{d} & 40^{\circ} \end{array} $$

Can you prove that two parallelograms are congruent by proving that all their corresponding sides are congruent? Explain your reasoning.

PROVING A THEOREM Prove the Parallelogram Diagonals Converse Theorem 7.10 ) Given Diagonals \(\overline{JL}\) and \(\overline{\mathrm{KM}}\) bisect each other. Prove JKLM is a parallelogram.

DRAWING CONCLUSIONSVhich of the following angle measures are possible interior angle measures of a regular polygon? Explain your reasoning. Select all that apply. \(A 162^{\circ}\) \(B 171^{\circ}$$C 75^{\circ}$$D 40^{\circ}\)

REASONING Three interior angle measures of a quadrilateral are \(67^{\circ}, 67^{\circ}\) , and \(113^{\circ}\) . Is this enough information to conclude that the quadrilateral is a parallelogram? Explain your reasoning.

MAKING AN ARGUMEN POur friend claims that to I nd the interior angle measures of a regular polygon, you do not have to use the Polygon Interior Angles Theorem (Theorem 7.1). You instead can use the Polygon Exterior Angles Theorem (Theorem 7.2) and then the Linear Pair Postulate (Postulate 2.8 ). Is your friend correct? Explain your reasoning.