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# In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure  [#permalink]

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11 Jan 2019, 01:49
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69% (00:41) correct 31% (01:17) wrong based on 41 sessions

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In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure of ∠D?

A. 90
B. 120
C. 135
D. 270
E. It cannot be determined from the information given.

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Manager
Joined: 02 Aug 2015
Posts: 155
Re: In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure  [#permalink]

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11 Jan 2019, 02:32
Bunuel wrote:
In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure of ∠D?

A. 90
B. 120
C. 135
D. 270
E. It cannot be determined from the information given.

In a quadrilateral, sum of all angles is equal to 360.

∠A +∠B + ∠C +∠D = 360.
Given ∠A +∠B + ∠C = 2∠D
So 3∠D = 360
∠D = 120.

Hence B.

Cheers!
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Joined: 18 Aug 2017
Posts: 3879
Location: India
Concentration: Sustainability, Marketing
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Re: In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure  [#permalink]

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11 Jan 2019, 04:31
Bunuel wrote:
In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure of ∠D?

A. 90
B. 120
C. 135
D. 270
E. It cannot be determined from the information given.

a+b+c+d= 360
2d=360
d=120
IMO B
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Manager
Joined: 18 Oct 2018
Posts: 83
Location: India
Concentration: Finance, International Business
GPA: 4
WE: Business Development (Retail Banking)
Re: In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure  [#permalink]

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11 Jan 2019, 12:14
In a quadrilateral, sum of all angles is equal to 360.

∠A +∠B + ∠C +∠D = 360.
Given ∠A +∠B + ∠C = 2∠D
So 3∠D = 360
∠D = 120.

Hence B.
Re: In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure   [#permalink] 11 Jan 2019, 12:14
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# In quadrilateral ABCD, ∠A +∠B + ∠C = 2∠D. What is the degree measure

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