i rewrited the question.
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Given,
<POR : <ROM = 1:5 = 1A : 5A
By the angle property of straight line
<POR + <ROM = 180
1A + 5A = 180
6A = 180
A = 30 degree
Hence: <POR = 30, <ROM = 150
<UMQ : <UMO = 2 : 7 = 2B : 7B
Again by angle property,
<UMQ + <UMO = 180
9B = 180
B = 20
Hence, <UMQ = 40, <UMO = 140
<ROP + <POS = 180
30 + X = 180
X = 150
<UMQ + <QMN = 180
40 + Y = 180
Y = 140
In traingle OMN
<MON = 180 - X = 30
<OMN = 180 - Y = 40
<MON + <OMN + <ONM = 180
30 + 40 +<ONM = 180
<ONM = 110.....
<ONM = Z = 110...[vertically opposite angles]
X= 150, Y = 140, Z = 110
X+Y+Z = 150 + 140 + 110 = 400.
Hope it helps.
<POR : <ROM = 1:5 = 1A : 5A
By the angle property of straight line
<POR + <ROM = 180
1A + 5A = 180
6A = 180
A = 30 degree
Hence: <POR = 30, <ROM = 150
<UMQ : <UMO = 2 : 7 = 2B : 7B
Again by angle property,
<UMQ + <UMO = 180
9B = 180
B = 20
Hence, <UMQ = 40, <UMO = 140
<ROP + <POS = 180
30 + X = 180
X = 150
<UMQ + <QMN = 180
40 + Y = 180
Y = 140
In traingle OMN
<MON = 180 - X = 30
<OMN = 180 - Y = 40
<MON + <OMN + <ONM = 180
30 + 40 +<ONM = 180
<ONM = 110.....
<ONM = Z = 110...[vertically opposite angles]
X= 150, Y = 140, Z = 110
X+Y+Z = 150 + 140 + 110 = 400.
Hope it helps.
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