Question

what is the value of , 36 degrees or 30 degrees? figure is on the first comment.

Answer 1

hmm

Answer 2

what leads you to those two options?

Answer 3

use this \[ \sqrt{3}/4\]

Answer 4

it is for =ilatarel triangle

Answer 5

Angle sum of a n-sided polygon \[ (n-2)\times 180°\]so for a pentagon angle sum is 540°

so each corner of the pentagon is 540°/5=110°

Answer 6

so if we let the inner angle be y
2x+y=110°

Answer 7

ya @UnkleRhaukus is right! ;-)

Answer 8

now the angle y looks a bit bigger than x so
if we set y=x+b

if \[x=36°\]\[110°=2 \times36° + 36° +b \]\[110°=108°+b\]\[b=2°\]

if \[x=30°\]\[110°=2 \times30° + 30° +b \]\[110°=90°+b\]\[b=20°\]

looking at the angles i reckon the first option looks more reasonable

Answer 9

there is probably a more mathematical proof

Answer 10

how can we use \[√3/4\] @Rohangrr

Answer 11

x=36

Answer 12

yes but how @cinar?

Answer 13

i knew it, the intercepted arc of x is 72 degrees so x is 36 degrees, and there is a postulate to prove that, i just forgot the name of postulate... another way to solve it is because of the isoceles triangle, 108+2x=180, x =36

Answer 14

3x=108

Answer 15

i see now
5x=180