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

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Math Expert
Joined: 02 Sep 2009
Posts: 58325
In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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19 Mar 2018, 01:43
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Difficulty:

25% (medium)

Question Stats:

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

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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 [ 5.35 KiB | Viewed 1071 times ]

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Math Expert
Joined: 02 Sep 2009
Posts: 58325
Re: In the figure, PSQ is a straight line and RS is perpendicular to ST.  [#permalink]

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19 Mar 2018, 01:44
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

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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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.

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

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

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

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20 Mar 2018, 16:55
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

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

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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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