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. ?

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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. ?

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Answer 1 · 2018-06-16T19:58:54

$205^@$

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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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. ?

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Explanation:

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Two interior angles AA and BB of pentagon ABCDEABCDE are 60^{\circ}60^{\circ} and 85^{\circ}85^{\circ}. Two of the remaining angles, CC and DD, are equal and the fifth angle EE is 15^{\circ}15^{\circ} more than twice CC. Find the measure of the largest angle. ?

1 Answer

Explanation:

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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. ?