Two interior angles #A# and #B# of pentagon #ABCDE# are #60^{\circ}# and #85^{\circ}#. Two of the remaining angles, #C# and #D#, are equal and the fifth angle #E# is #15^{\circ}# more than twice #C#. Find the measure of the largest angle. ?

1 Answer
Jim G.
Jun 16, 2018

#205^@#

Explanation:

#"the "color(blue)"sum of the interior angles of a polygon"# is.

#"sum "=180^@xx(n-2)#

#"where n is the number of sides"#

#"here "n=5larrcolor(red)"pentagon has 5 sides"#

#"sum "=180^@xx3=540^@#

#"let "C=D=x#

#"then "E=2x+15larrcolor(blue)"15 more than twice C"#

#"we can express the sum of the 5 angles as"#

#60+85+x+x+2x+15=540#

#"simplify left side by collecting like terms"#

#4x+160=540#

#"subtract 160 from both sides"#

#4xcancel(+160)cancel(-160)=540-160#

#4x=380#

#"divide both sides by 4"#

#(cancel(4) x)/cancel(4)=380/4rArrx=95#

#C=D=x=95^@#

#E=(2xx95)+15=205^@#

#"the 5 interior angles of the pentagon are"#

#60^@,85^@,95^@,95^@,205^@=540^@#

#"the largest angle is "E=205^@#

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