a line segment is drawn from the center of a regular pentagon to each of the five vertices, forming five congruent isoceles triangles. How many degrees are in each base angle?
2007-01-07 11:16:28 · 9 answers · asked by hoopmaster1 1 in Science & Mathematics ➔ Mathematics
The sum of the angles in the middle is 360°, so each angle must be 360°/5 = 72°.
Then, since the triangles are isoceles, their base angles are the same.
72° + x + x = 180°
2x = 180° - 72° = 108°
x = 54°
2007-01-07 11:21:56 · answer #1 · answered by Jim Burnell 6 · 0⤊ 0⤋
Using the Sum of Interior Angels formula, we can see that a pentagon has interior angles totalling=>180(5-2)=180(3)=540 degrees.
there are 10 base angles of equal degrees, so 10x=540, each base angel = 54 degrees..
2007-01-07 19:21:49 · answer #2 · answered by ArdentAzn 2 · 1⤊ 0⤋
540 degrees of angle in a pentagon so you divide that by 5 (the number of sides) which gives each angle a degree of 108. divide that by 2 (the line you draw from the center to it) and you get 54 degree angles. each base angle of the triangles will be 52 degrees, and the center angles will eache be 76
2007-01-07 19:21:53 · answer #3 · answered by Dashes 6 · 0⤊ 0⤋
i think 5 identical triangles wil be formed with angles 72,54,54... i dont really know which angle you mean
the 72 angle comes from 360/5... the 54 angles comes from (180-72)/2
hope this answers your question :)
2007-01-07 19:20:28 · answer #4 · answered by Mr singh 2 · 1⤊ 0⤋
72
2007-01-07 19:18:20 · answer #5 · answered by goodtimefriend 3 · 0⤊ 2⤋
360*/5= 72*
2007-01-07 19:21:18 · answer #6 · answered by w4gy 1 · 0⤊ 2⤋
been many decades but i will venture 36 degrees.
2007-01-07 19:21:44 · answer #7 · answered by Anonymous · 0⤊ 1⤋
54º, need proof?
e-mail me at kimjay_lmr01@yahoo.com
2007-01-07 19:20:30 · answer #8 · answered by kimjay_lmr01 1 · 0⤊ 0⤋
72degrees
2007-01-07 19:20:46 · answer #9 · answered by Navyant 2 · 0⤊ 2⤋