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

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

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New post 25 May 2016, 03:39
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

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

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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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New post 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
Answer B

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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New post 26 Jun 2016, 04:26
Bunuel wrote:
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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

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

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

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