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The exterior angles of a polygon can be reproduced together, so that they have the same vertex. To do this, draw lines parallel to the sides of the polygon from a point, as shown in Fig. 4-52. If this is done, it can be seen that regardless of the number of sides, the sum of the measures of the exterior angle equals 360 . Hence: Sum of measures of exterior angles of a polygon of n sides 360



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The basic principle of separation of duties is evident in the speci c con trols for cash balances: 1. Bank reconciliations should be prepared by persons who do not receive cash or sign checks. 2. Bank statements and paid checks should be received unopened by the person reconciling the account. 3. All cash funds on hand should be closely watched and surprise counts be made at intervals. If the requirement that all cash receipts be banked is followed, then it is clear that the monthly bank statement can be made a powerful con trol over cash balances.

Fig. 4-52

PRINCIPLE 1:

If S is the sum of the measures of the interior angles of a polygon of n sides, then S n 2 straight angles (n 2)180

The sum of the measures of the interior angles of a polygon of 10 sides (decagon) equals 1440 , since 8(180) 1440.





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The charset parameter of application/xml-external-parsedentity is handled the same as that of application/xml, as described in application/xml. Interoperability considerations are the same as those for text/xml-external-parsed-entity, as described in application/ xml. The published speci cation and applications that use this media type are the same as fortext/xml.

PRINCIPLE 2:

PRINCIPLE 3:

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Checks A business opens a checking account to gain the privilege of placing its deposits in a safe place and the ability also to write checks. When an ac count is opened, each person who is authorized to write checks on that account must sign a signature card. The bank keeps the signature card on le and compares it when checks are submitted. The check becomes a written notice by the depositor directing the bank to deduct a speci c sum of money from the checking account and to pay that amount to the per son or company written on the check. A check involves three parties: 1. Drawer the rm that writes the check 2. Drawee the bank on which the check is drawn 3. Payee the person or company to whom the check is paid. Checks offer several advantages. The checkbook stubs provide a record of the cash paid out, while the canceled checks provide proof that money has been paid to the person legally entitled to it. Also, the use of checks is the most convenient way of paying bills, because checks can safely be sent through the mail.

If a regular polygon of n sides (Fig. 4-53) has an interior angle of measure i and an exterior angle of measure e (in degrees), then 180(n n 2) 360 n , and i

Fig. 4-53

Thus for a regular polygon of 20 sides, 180(20 20 2) 360 20

4.15 Applying angle-measure formulas to a polygon (a) Find the sum of the measures of the interior angles of a polygon of 9 sides (express your answer in straight angles and in degrees). (b) Find the number of sides a polygon has if the sum of the measures of the interior angles is 3600 . (c) Is it possible to have a polygon the sum of whose angle measures is 1890

(a) S (in straight angles) (b) S (in degrees) (c) Since 1890 n 2 9 2 7 straight angles; mjS (n 2)180 22. sides. 7(180) 1260 .

1 122

4.16 Applying angle-measure formulas to a regular polygon (a) Find each exterior angle measure of a regular polygon having 9 sides. (b) Find each interior angle measure of a regular polygon having 9 sides. (c) Find the number of sides a regular polygon has if each exterior angle measure is 5 . (d) Find the number of sides a regular polygon has if each interior angle measure is 165 .

If a check is lost or stolen, the de positors can request the bank not to pay (a stop order).

180 40

4.17 Applying algebra to the angle-measure sums of a polygon Find each interior angle measure of a quadrilateral (a) if its interior angles are represented by x 2x 20, 3x 50, and 2x 20; (b) if its exterior angles are in the ratio 2:3:4:6.

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