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If ABCDE is a regular pentagon, what is the measure of EBD? 30° 36°

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If ABCDE is a regular pentagon, what is the measure of EBD? 30° 36° [#permalink] New post   31 May 2022, 01:00
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If ABCDE is a regular pentagon, what is the measure of \(\angle EBD\)?


30°
36°
45°
72°
108°


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Re: If ABCDE is a regular pentagon, what is the measure of EBD? 30° 36° [#permalink] New post   31 May 2022, 06:53
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A regular pentagon has a total angle measure of (n-2)180 = (5-2)180 = 540 degrees.

Since each of these angles are the same (that is the meaning of "regular" here), then we know that each of the angles is 540/5 = 108 degrees.

If the two lines from E to B and from D to B are straight lines, then they must trisect (cut into three even pieces) the 108-degree angle at B. That means that the angle in question, angle EBD, must be 108/3 = 36 degrees. Answer B.
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Re: If ABCDE is a regular pentagon, what is the measure of EBD? 30° 36° [#permalink] New post   12 May 2024, 09:29
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Re: If ABCDE is a regular pentagon, what is the measure of EBD? 30° 36° [#permalink]
12 May 2024, 09:29
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