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# In the figure to the right, the sum of the measures of angles PQR and

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Math Expert
Joined: 02 Sep 2009
Posts: 64249
In the figure to the right, the sum of the measures of angles PQR and  [#permalink]

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25 May 2016, 03:39
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Difficulty:

15% (low)

Question Stats:

86% (02:31) correct 14% (02:56) wrong based on 42 sessions

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In the figure to the right, the sum of the measures of angles PQR and PRQ is 150 degrees. How many degrees greater is the measure of angle PRS than the measure of angle PQR?

A. 20
B. 30
C. 40
D. 50
E. 60

Attachment:

PS028Q.gif [ 2.22 KiB | Viewed 1367 times ]

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Re: In the figure to the right, the sum of the measures of angles PQR and  [#permalink]

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25 May 2016, 05:41
1
$$\angle$$ 1 + $$\angle$$ 2 = 150
=> $$\angle$$ QPR = 180 - 150 = 30
Also $$\angle$$ 1 + $$\angle$$ 2 + $$\angle$$ QPR = 180 -- equation 1
$$\angle$$2 + $$\angle$$ 3 = 180 (Linear Pair axiom ) -- equation 2

From equations 1 and 2 , we get
$$\angle$$ 3 = $$\angle$$1 + $$\angle$$QPR
=> $$\angle$$ 3 - $$\angle$$ 1 = $$\angle$$ QPR = 30

Also , we can use a property that an exterior angle of a triangle is equal to sum of interior opposite angles to reach the equation we have derived from equations 1 and 2
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Re: In the figure to the right, the sum of the measures of angles PQR and  [#permalink]

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26 Jun 2016, 04:26
Bunuel wrote:

In the figure to the right, the sum of the measures of angles PQR and PRQ is 150 degrees. How many degrees greater is the measure of angle PRS than the measure of angle PQR?

A. 20
B. 30
C. 40
D. 50
E. 60

Attachment:
PS028Q.gif

need to find ∠PRS-∠PQR=?
∠PRS+∠PRQ=180
∠PRS+150-∠PQR=180(given ∠PRQ+∠PQR=150)
∠PRS-∠PQR=30
Ans B
Re: In the figure to the right, the sum of the measures of angles PQR and   [#permalink] 26 Jun 2016, 04:26