Find this angle?

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1 Answer
Jan 28, 2018

Use these facts:
The interior angle of a regular pentagon is #108^@#
The lines of symmetry bisect the angles and are perpendicular to the opposite side.

Explanation:

Let O be the point where the two lines intersect.

The facts allow us to find the angles for the triangle formed by AOC:

#54^@# because the #108^@# angle is bisected

#90^@#, because the line of symmetry is perpendicular to that side.

This gives us the #angle AOC = 180^@-54^@-90^@ = 36^@#

#angle AOC# is supplemental to #angle x#:

#angle x = 180^@-36^@#

#angle x = 144^@#