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If the degree measures of the four angles of a quadrilateral are in th

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If the degree measures of the four angles of a quadrilateral are in th [#permalink]

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New post 28 Sep 2017, 23:47
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If the degree measures of the four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4, what is the degree measure of the largest angle?

(A) 36
(B) 90
(C) 144
(D) 160
(E) 180
[Reveal] Spoiler: OA

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If the degree measures of the four angles of a quadrilateral are in th [#permalink]

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New post 29 Sep 2017, 15:59
Bunuel wrote:
If the degree measures of the four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4, what is the degree measure of the largest angle?

(A) 36
(B) 90
(C) 144
(D) 160
(E) 180

To find the degree measure of the largest angle, take the ratio of the angles, sum the ratio's parts, and find the multiplier.

Angles' ratio: 1x: 2x: 3x: 4x
Add them
Ratio parts' total: 10x

The sum of the interior angles of a quadrilateral is 360 degrees. (Sum of interior angles of a polygon, where n is number of sides, is (n- 2) * 180 degrees)

10x = 360
x = 36, the multiplier in degrees

The largest angle is 4x
(4)(36°) = 144°

Answer C

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Re: If the degree measures of the four angles of a quadrilateral are in th [#permalink]

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New post 30 Sep 2017, 00:58
Bunuel wrote:
If the degree measures of the four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4, what is the degree measure of the largest angle?

(A) 36
(B) 90
(C) 144
(D) 160
(E) 180


Sum of the ratio numbers = 1+2+3+4 = 10 which is actually equal to 360 degrees (sum of angles in a quadrilateral)

Since 10 = 360 degrees
so biggest of four angles 4 = (360/10)*4 = 144 degrees

answer:Option C
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Re: If the degree measures of the four angles of a quadrilateral are in th   [#permalink] 30 Sep 2017, 00:58
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