2. In the given figure, l || m and t is a transversal. If 41 and 22. are
in the ratio 5 : 7, find the measure of each of the angles
cs for Class 7
178
4. 2. 23 and 28.
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Answer:
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
o
∠3+∠6=180
o
......[∵ the sum of the consecutive interioi angles is 180
o
]
75
o
+∠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
o
,∠2=105
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,∠=75
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and ∠8=105
o
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