Question

2. In the given figure, 1 || m and t is a transversal. If 41 and 22 are
in the ratio 5 : 7. find the measure of each of the 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

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

.