4. In the given figure, 1 || m and n is a transversal angle1 = 115 and Angeles 2=110 parallel to m
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In the given figure. l∥ m and t is a transversal. If ∠1 and ∠2 are in the ratio 5:7, find the measure of each of the angle ∠1,∠2,∠3 and ∠8
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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
o
+∠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
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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