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

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Math Expert
Joined: 02 Sep 2009
Posts: 46217
If the degree measures of the four angles of a quadrilateral are in th [#permalink]

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28 Sep 2017, 23:47
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96% (00:31) correct 4% (00:00) wrong based on 28 sessions

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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

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Posts: 1757
If the degree measures of the four angles of a quadrilateral are in th [#permalink]

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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
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°

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

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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

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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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