Question

In the figure l parallel to m is angle 1=40 degrees then angle 6 is ​

Answer 1

Step-by-step explanation:

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

.

Answer 2

Given,

∠1 = 40°

Then,

$\text{∠3 = ∠1 = 40° }\text{ \{vertically opposite ∠s\}}$

And,

∠3 + ∠6 = 180° {co-interior ∠s}

→ 40° + ∠6 = 180°

→ ∠6 = 180° - 40°

→ ∠6 = 140°