Question #f3de6

1 Answer
Feb 11, 2018

The angle measures of the pentagon are #75^@#, #90^@#, #105^@#, #120^@#, and #150^@#.

Explanation:

I'm assuming that these five angles are from a pentagon.

We know that the sum of the interior angles in a polygon is #(n-2)*180^@# where #n# is the number of sides in the polygon. Therefore, in a pentagon, the sum of the interior angles is

#(5-2)*180^@=3*180^@=540^@#

Since the angles' ratio is #5x:6x:7x:8x:10x#, we know that their sum must be #540^@#:

#5x+6x+7x+8x+10x=540^@#

#36x=540^@#

#x=15^@#

Now we can find all the angle measures by multiplying #12^@# by #5#, #6#, #7#, #8#, and #10#:

#mangle1=15^@*5=75^@#

#mangle2=15^@*6=90^@#

#mangle3=15^@*7=105^@#

#mangle4=15^@*8=120^@#

#mangle5=15^@*10=150^@#

We can check our answer by seeing if the sum of these angles is still #540^@#:

#color(red)(75^@+90^@)+color(blue)(105^@+120^@+150^@)=540^@#

#color(red)(165^@)+color(blue)(375^@)=540^@#

#color(purple)(540^@)=540^@#

Since this expression is true, our answer is correct.