Question

In the figure, L is parallel to M and T is a transversal. If angle 1 and angle 2 are in the ratio of 5:7, find the measure of the following angles : 1,2,3 and 8​

Answer 1

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 degree

∠2=7x=7×15=150 degree

We know that,

∠2+∠3=180 degree

......[∵ linear pair]

105 degree +∠3=180 degree

=∠3=180−105

∠3=75 degree

∠3+∠6=180 degree

......[∵ the sum of the consecutive interior angles is 180 degree

75 degree +∠5=180 degree

∠6=180−75

∠6=150 degree

Now ∠6=∠8=150 degree

.....[∵ vertically opposite angles are equal]

∴∠1=75 degree,

∠2=105 degree,

∠=75 degree

and ∠8=105 degree.

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