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In the figure, PSQ is a straight line and RS is perpendicular to ST.

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In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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New post 19 Mar 2018, 01:43
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

86% (01:04) correct 14% (02:58) wrong based on 40 sessions

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Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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New post 19 Mar 2018, 01:44
Bunuel wrote:
Image
In the figure, PSQ is a straight line and RS is perpendicular to ST. If the measure of angle RSQ = 48°, how many degrees are there in angle PST?

A. 48
B. 90
C. 132
D. 136
E. 138

Attachment:
2018-03-19_1041.png


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Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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New post 19 Mar 2018, 01:50
Bunuel wrote:
In the figure, PSQ is a straight line and RS is perpendicular to ST. If the measure of angle RSQ = 48°, how many degrees are there in angle PST?

A. 48
B. 90
C. 132
D. 136
E. 138



As our calculation is straightforward, we'll just do it.
This is a Precise approach.

\(\angle\)PST = 360 - \(\angle\)RST - \(\angle\)RSP
We're told that \(\angle\)RST = 90 and we can calculate \(\angle\)RSP as 180 - 48 = 132.
Then \(\angle\)PST = 360 - 90 - 132 = 138.

(E) is our answer.
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Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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New post 19 Mar 2018, 13:55
Given ∠RST = 90
=> ∠QST = 90-48 = 42
Now, ∠QST+∠PST= 180
So, ∠PST=180-∠QST= 180-42 = 138

Hence answer is E
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Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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New post 20 Mar 2018, 16:55
Bunuel wrote:
Image
In the figure, PSQ is a straight line and RS is perpendicular to ST. If the measure of angle RSQ = 48°, how many degrees are there in angle PST?

A. 48
B. 90
C. 132
D. 136
E. 138

Attachment:
2018-03-19_1041.png


Since angle PST + angle TSQ = 180 degrees, and since angle TSQ is 90 - 48 = 42 degrees, angle PST is:

180 - 42 = 138 degrees

Answer: E
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Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.   [#permalink] 20 Mar 2018, 16:55
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