3. In the given figure, / || m and p is the
transversal. If 21 and 22 are in the ratio
1:2, find the measure of each of the angles,
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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
o
......[∵ linear pair]
150
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+∠3=180
o
=∠3=180−105
∠3=75
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∠3+∠6=180
o
......[∵ the sum of the consecutive interioi angles is 180
o
]
75
o
+∠5=180
o
∠6=180−75
∠6=150
o
Now ∠6=∠8=150
o
.....[∵ vertically opposite angles are equal]
∴∠1=75
o
,∠2=105
o
,∠=75
o
and ∠8=105
o
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