If in adjoining figure, l||m and angle 2=125°, Find measure of angle 8. is angle 8=angle 2
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Two parallel lines l and m be cut a transversal t, forming angles.
It is given that ∠1:∠2=5:7
Let the measures of angles by 5x and 7x,
Then,
5x+7x=180
12x=180
x=180/12
x=15
∴∠1=5x=5×15=75
o
∠2=7x=7×15=150
o
We know that,
∠2+∠3=180
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.[∵ linear pair]
150
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+∠3=180
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=∠3=180−105
∠3=75
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∠3+∠6=180
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...[∵ the sum of the consecutive interioi angles is 180
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]
75
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+∠5=180
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∠6=180−75
∠6=150
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Now ∠6=∠8=150
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.[∵ vertically opposite angles are equal]
∴∠1=75
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,∠2=105
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,∠=75
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and ∠8=105
o
.
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