Question

In the figure, ABCDE is a regular pentagon. CFD is equilateral and EFX is a straight line. Find angle FXB

Answer 1

CFD is equilateral

so what are the measures of these angles

CFD
FDC
DCF

Answer 2

Im assuming that if it is a regular pentagon, each interior angle is:
\[\frac{ 360^{o} }{ 5 }= 72^{o}\]
And each angle is the equilateral is 60 so we have something like this
this is as far as I am able to go and I do not guarantee it is correct

Answer 3

each interior angle is 108

180 - 72 = 108

72 is the measure of each exterior angle

Answer 4

angle FDE is 48
hence angles DFE and DEF are both 66

Answer 5

@jim_thompson5910 you are right...thanks

Answer 6

this makes angle XFC 54
and hence angle CXF is 78
do you follow?

Answer 7

angle CXF is 78 because angle FCX is 48

Answer 8

and so you can now work out angle FXB

Answer 9

thanks everybody