Question

In the given figures L || m and angles 1 and 2 in the ratio 2:1. determine angle 4 and angle 7​

Answer 1

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°

∠2=7x=7×15=150°

We know that,

∠2+∠3=180°

[∵ linear pair]

150° +∠3=180°

=∠3=180−105

∠3=75°

∠3+∠6=180°

[∵ the sum of the consecutive interioi angles is 180°]

75°+∠5=180°

∠6=180−75

∠6=150°

Now ∠6=∠8=150°

[∵ vertically opposite angles are equal]

∴∠1=75° ,∠2=105° ,∠=75°and ∠8=105°