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# In the figure, ∠P =

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Math Expert
Joined: 02 Sep 2009
Posts: 61544
In the figure, ∠P =  [#permalink]

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12 Mar 2019, 22:42
00:00

Difficulty:

5% (low)

Question Stats:

94% (00:54) correct 6% (01:43) wrong based on 32 sessions

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In the figure, ∠P =

(A) 15°

(B) 30°

(C) 35°

(D) 40°

(E) 50°

Source: Nova GMAT
Difficulty Level: 500

Attachment:

#GREpracticequestion In the figure, ∠P =.jpg [ 35.03 KiB | Viewed 558 times ]

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Re: In the figure, ∠P =  [#permalink]

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12 Mar 2019, 22:58

Concepts used:
1. Angles in a line sum up to 180°
2. Sum of angles in a triangle is 180°

∠PAD = 180° - 105° = 75° | ∠PDA = 180° - 115° = 65°

Also, In Triangle PAD, ∠PAD + ∠A + ∠PDA = 180°

Therefore, in the figure, ∠P = 180° - 140° = 40°(Option D)
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Re: In the figure, ∠P =  [#permalink]

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13 Mar 2019, 02:05
Bunuel wrote:

In the figure, ∠P =

(A) 15°

(B) 30°

(C) 35°

(D) 40°

(E) 50°

Attachment:
#GREpracticequestion In the figure, ∠P =.jpg

from given info
we can determine angles of the triangle = 75 & 65
so angle P = 180-140 ; 40
IMO D
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Joined: 25 Feb 2019
Posts: 333
Re: In the figure, ∠P =  [#permalink]

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13 Mar 2019, 03:04
IMO D .

ABCD is a cyclic quadrilateral , so opposite angles will have sum 180.

This way we can find the angle B and C

and then find angle P via triangle sum property

180-(65+75)= 40

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Re: In the figure, ∠P =  [#permalink]

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18 Mar 2019, 05:17
Bunuel wrote:

In the figure, ∠P =

(A) 15°

(B) 30°

(C) 35°

(D) 40°

(E) 50°

Attachment:
#GREpracticequestion In the figure, ∠P =.jpg
Angle A is 180 - 105 = 75 degrees

Angle D is 180 - 115 = 65 degrees.

Thus angle P is 180 - 75 - 65 = 40 degrees.

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Re: In the figure, ∠P =   [#permalink] 18 Mar 2019, 05:17
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