VOCABULARYWhy do vertices connected by a diagonal of a polygon have to be nonconsecutive?

Ali S.

Numerade Educator

WHICH ONE DOESN'T BELONGYhich sum does not belong with the other three? Explain

your reasoning.

Sachit K.

Numerade Educator

In Exercises $3-6,$ ind the sum of the measures of the interior angles of the indicated convex polygon.

(See Example 1.)

nonagon

Ali S.

Numerade Educator

In Exercises $3-6,$ ind the sum of the measures of the interior angles of the indicated convex polygon.

(See Example 1.)

14 -gon

Sachit K.

Numerade Educator

In Exercises $3-6,$ ind the sum of the measures of the interior angles of the indicated convex polygon.

(See Example 1.)

$16-\mathrm{gon}$

Ali S.

Numerade Educator

In Exercises $3-6,$ ind the sum of the measures of the interior angles of the indicated convex polygon.

(See Example 1.)

20 -gon

Sachit K.

Numerade Educator

In Exercises $7-10$ , the sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. (See Example $2 .$ )

$$

720^{\circ}

$$

Ali S.

Numerade Educator

In Exercises $7-10$ , the sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. (See Example $2 .$ )

$$

1080^{\circ}

$$

Sachit K.

Numerade Educator

In Exercises $7-10$ , the sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. (See Example $2 .$ )

$$

2520^{\circ}

$$

Ali S.

Numerade Educator

In Exercises $7-10$ , the sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides. (See Example $2 .$ )

$$

3240^{\circ}

$$

Sachit K.

Numerade Educator

In Exercises $11-14,$ ind the value of $\mathrm{x}$ . (See Example $3 . )$

Ali S.

Numerade Educator

In Exercises $11-14,$ ind the value of $\mathrm{x}$ . (See Example $3 . )$

Sachit K.

Numerade Educator

In Exercises $11-14,$ ind the value of $\mathrm{x}$ . (See Example $3 . )$

Ali S.

Numerade Educator

In Exercises $11-14,$ ind the value of $\mathrm{x}$ . (See Example $3 . )$

Sachit K.

Numerade Educator

In Exercises $19-22,$ ind the measures of $\angle \mathrm{X}$ and $\angle \mathrm{Y}$ .

(See Example 4.)

Ali S.

Numerade Educator

(See Example 4.)

Sachit K.

Numerade Educator

(See Example 4.)

Ali S.

Numerade Educator

(See Example 4.)

Sachit K.

Numerade Educator

In Exercises $23-26,$ i ind the value of $\mathrm{x}$ . (See Example $5 . )$

Ali S.

Numerade Educator

In Exercises $23-26,$ i ind the value of $\mathrm{x}$ . (See Example $5 . )$

Sachit K.

Numerade Educator

In Exercises $23-26,$ i ind the value of $\mathrm{x}$ . (See Example $5 . )$

Ali S.

Numerade Educator

In Exercises $23-26,$ i ind the value of $\mathrm{x}$ . (See Example $5 . )$

Sachit K.

Numerade Educator

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

pentagon

Ali S.

Numerade Educator

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

Sachit K.

Numerade Educator

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

$45-\operatorname{gon}$

Ali S.

Numerade Educator

In Exercises $27-30,$ ind the measure of each interior angle and each exterior angle of the indicated regular polygon. (See Example $6 .$ )

90 -gon

Sachit K.

Numerade Educator

ERROR ANALYSISn Exercises 31 and $32,$ describe and correct the error in I nding the measure of one exterior angle of a regular pentagon.

figure can't copy

Ali S.

Numerade Educator

ERROR ANALYSISn Exercises 31 and $32,$ describe and correct the error in finding the measure of one exterior angle of a regular pentagon.

figure can't copy

Sachit K.

Numerade Educator

MODELING WITH MATHEMATIGß base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior angle of the jewelry box base?

Ali S.

Numerade Educator

MODELING WITH MATHEMATIGSe loor of the gazebo shown is shaped like a regular decagon.

Find the measure of each interior angle of the regular decagon. Then I nd the measure of each exterior angle.

Sachit K.

Numerade Educator

WRITING A FORMULAVrite a formula to ind the number of sides n in a regular polygon given that the

measure of one interior angle is $\mathrm{x}^{\circ}$ .

Ali S.

Numerade Educator

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 $x^{\circ}$ .

Sachit K.

Numerade Educator

REASONINGIn Exercises $37-40,$ i nd the number of sides for the regular polygon described.

Each interior angle has a measure of $156^{\circ} .$

Ali S.

Numerade Educator

REASONINGIn Exercises $37-40,$ i nd the number of sides for the regular polygon described.

Each interior angle has a measure of $165^{\circ}$

Sachit K.

Numerade Educator

REASONINGIn Exercises $37-40,$ i nd the number of sides for the regular polygon described.

Each exterior angle has a measure of $9^{\circ} .$

Ali S.

Numerade Educator

REASONINGIn Exercises $37-40,$ i nd the number of sides for the regular polygon described.

Each exterior angle has a measure of $6^{\circ} .$

Sachit K.

Numerade Educator

PROVING A THEOREMhe Polygon Interior Angles Theorem (Theorem 7.1) states that the sum of the

measures of the interior angles of a convex n-gon is $(\mathrm{n}-2) \cdot 180^{\circ} .$ Write a paragraph proof of this theorem for the case when $\mathrm{n}=5$

Ali S.

Numerade Educator

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}$

Sachit K.

Numerade Educator

PROVING A COROLLARWrite a paragraph proof of the Corollary to the Polygon Interior Angles Theorem

(Corollary 7.1$)$

Ali S.

Numerade Educator

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.

Sachit K.

Numerade Educator

MATHEMATICAL CONNECTIONSan equilateral hexagon, four of the exterior angles each have a

measure of $x^{\circ}$ . The other two exterior angles each have a measure of twice the sum of $x$ and $48 .$ Find the measure of each exterior angle.

Ali S.

Numerade Educator

THOUGHT PROVOKINGF of a concave polygon, is it true that at least one of the interior angle measures

must be greater than $180^{\circ}$ ? If not, give an example. If so, explain your reasoning.

Sachit K.

Numerade Educator

WRITING EXPRESSIONSVrite an expression to $\mathrm{nd}$ the sum of the measures of the interior angles for a concave polygon. Explain your reasoning.

Ali S.

Numerade Educator

ANALYZING RELATIONSHIPSIygon ABCDEFGH is a regular octagon. Suppose sides $\overline{A B}$ and $\overline{C D}$ are extended to meet at a point $P .$ Find $m \angle B P C$ . Explain your reasoning. Include a diagram with your answer.

Sachit K.

Numerade Educator

MULTIPLE REPRESENTATIONSE formula for the measure of each interior angle in a regular polygon

can be written in function notation.

a. Write a function $\mathrm{h}(\mathrm{n}),$ where $\mathrm{n}$ is the number of sides in a regular polygon and $\mathrm{h}(\mathrm{n})$ is the measure of any interior angle in the regular polygon.

b. Use the function to $\operatorname{nd} \mathrm{h}(9)$ .

c. Use the function to nd n when $h(n)=150^{\circ} .$

d. Plot the points for $n=3,4,5,6,7,$ and $8 .$ What happens to the value of h(n) as n gets larger?

Ali S.

Numerade Educator

HOW DO YOU SEE ITTs the hexagon a regular hexagon? Explain your reasoning.

Sachit K.

Numerade Educator

PROVING A THEOREMVrite a paragraph proof of the Polygon Exterior Angles Theorem (Theorem 7.2).

(Hint: In a convex n-gon, the sum of the measures of an interior angle and an adjacent exterior angle at any vertex is 180 )

Ali S.

Numerade Educator

ABSTRACT REASONINGOu are given a convex polygon. You are asked to draw a new polygon by

increasing the sum of the interior angle measures by $540^{\circ}$ . How many more sides does your new polygon have? Explain your reasoning.

Sachit K.

Numerade Educator

Find the value of $\mathrm{x}$ . (Section 3.2$)$

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Ali S.

Numerade Educator

Find the value of $\mathrm{x}$ . (Section 3.2$)$

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Sachit K.

Numerade Educator

Find the value of $\mathrm{x}$ . (Section 3.2$)$

graph can't copy

Ali S.

Numerade Educator

Find the value of $\mathrm{x}$ . (Section 3.2$)$

graph can't copy

Sachit K.

Numerade Educator