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Chapter 3: Q24 (page 105)

BC炉is one side of a regular n-gon. The sides next to BC炉 are extended to meet at W. Find the measure of 鈭�W in terms of n.

Short Answer

Expert verified

The measure of 鈭�Win terms of nis180掳n-4n

Step by step solution

01

Step 1. Draw the diagram of a regular n-gon in which sides next to BC are extended to meet at w.

The diagram of a regular n-gon in which sides next to BC炉 are extended to meet at W is:

02

Step 2. Description of step.

The measure of each exterior angle of a regular polygon with n sides is given by:

360掳n

03

Step 3. Description of step.

From the diagram it can be noticed that the angles 鈭�WBCand 鈭�WCBare the exterior angles of the regular n-gon.

Therefore, the measures of the angles 鈭�WBCand 鈭�WCBis 360掳n.

The sum of the angles of the triangle is 180掳.

Therefore, the sum of the angles of the triangle 螖WBCis 180掳.

Therefore, it can be obtained that:

鈭�WBC+鈭�WCB+鈭�BWC=180掳360掳n+360掳n+鈭�BWC=180掳720掳n+鈭�BWC=180掳鈭�BWC=180掳鈭�720掳n鈭�BWC=180掳n鈭�720掳n

Therefore, the measure of the angle 鈭�Win terms of is 180掳n鈭�4n.

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