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Chapter 3: Q24 (page 105)

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

Short Answer

Expert verified

The measure of ∠Win terms of nis180°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¯ 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°n

03

Step 3. Description of step.

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

Therefore, the measures of the angles ∠WBCand ∠WCBis 360°n.

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

Therefore, the sum of the angles of the triangle ΔWBCis 180°.

Therefore, it can be obtained that:

∠WBC+∠WCB+∠BWC=180°360°n+360°n+∠BWC=180°720°n+∠BWC=180°∠BWC=180°−720°n∠BWC=180°n−720°n

Therefore, the measure of the angle ∠Win terms of is 180°n−4n.

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Most popular questions from this chapter

Find the values of xand y

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Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name five lines that appear to be parallel toAG¯.
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