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13 Oct 2020, 07:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:37) correct
25%
(03:13)
wrong
based on 66
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, QR is parallel to ST. What is the measure of angle x?
A. 35
B. 45
C. 65
D. 70
E. 110
Attachment:
1.jpg [ 13.92 KiB | Viewed 4369 times ]
13 Oct 2020, 08:58
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Let the point of intersection of QR be U on line PS and V on line PT
Sum of the exterior angles of a polygon = 360
In triangle PUV, y + 115 + y + 25 = 360
2y = 360 - 140 = 220
y = 110
Since QR is \\ to ST, \(\angle{PVU}\) will be equal to x as they are corresponding angles.
\(\angle{PVU}\) = 180 - (y + 25), as they lie on the same line
Therefore x = 180 - (y + 25) = 180 - (110 + 25) = 180 - 135 = 45
Option B
Arun Kumar
Sum of the exterior angles of a polygon = 360
In triangle PUV, y + 115 + y + 25 = 360
2y = 360 - 140 = 220
y = 110
Since QR is \\ to ST, \(\angle{PVU}\) will be equal to x as they are corresponding angles.
\(\angle{PVU}\) = 180 - (y + 25), as they lie on the same line
Therefore x = 180 - (y + 25) = 180 - (110 + 25) = 180 - 135 = 45
Option B
Arun Kumar
13 Oct 2020, 20:30
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In the figure above, QR is parallel to ST. What is the measure of angle x?
A. 35
B. 45
C. 65
D. 70
E. 110
Explanation:
Applying external angle theorem in triangle PQR,
y=(180-115)+(180-y-25)
y=180+40-y
y=110
now QR is parallel to ST
so, angle PRQ=x
x=180-(y+25)
x=180-110-25
x=45
Hence B is the correct answer.
A. 35
B. 45
C. 65
D. 70
E. 110
Explanation:
Applying external angle theorem in triangle PQR,
y=(180-115)+(180-y-25)
y=180+40-y
y=110
now QR is parallel to ST
so, angle PRQ=x
x=180-(y+25)
x=180-110-25
x=45
Hence B is the correct answer.
14 Oct 2020, 10:44
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Bunuel
Focus on the 180-degree angles containing all the labeled values. There are three 180 degree angles we can add together, with the 3 unknown angles being the 3 interior angles of the triangle.
Thus we have: \(115 + y + y + 25 + 180 = 540\)
\(140 + 2y = 360\)
\(y = 220/2 = 110\)
Then x = 180 - (y + 25) = 180 - 135 = 45.
Ans: B
Attachments
3-180-degrees.png [ 15.61 KiB | Viewed 3570 times ]
