Question

In the given figure a and b are parallel lines and l is a transversal. If ∠2 = 70* , determine the other seven angles as marked. ​
PLEASE GIVE FULL EXPLANATION ​

Answer 1

1-35° the first answer of this question

Answer 2

$\large\underline{\sf{Solution-}}$

In the given figure, a and b are parallel lines and l is a transversal such that

$\sf \: \angle 2 = 70 \degree \:$

Now,

$\sf \: \angle 2 = \angle 4 \: \: \: \: \: \{vertically\:opposite\:angles \}$

$\bf\implies \:\angle 4 = 70\degree$

Again,

$\sf \: \angle 1 + \angle 2 = 180\degree \: \: \: \: \: \{Linear\:pair \}$

$\sf \: \angle 1 + 70\degree = 180\degree$

$\sf \: \angle 1 = 180\degree - 70\degree$

$\bf\implies \:\angle 1 = 110\degree$

Now,

$\sf \: \angle 1 = \angle 3 \: \: \: \: \: \{vertically\:opposite\:angles \}$

$\bf\implies \:\angle 3 = 110\degree$

Now,

As a || b and l is a transversal. We know, corresponding angles are equal.

So,

$\sf \: \angle 1 = \angle 5 \: \: \{corresponding \: angles \}$

$\bf\implies \:\angle 5 = 110\degree$

Also,

$\sf \: \angle 4 = \angle 8 \: \: \{corresponding \: angles \}$

$\bf\implies \:\angle 8 = 70\degree$

Now,

$\sf \: \angle 6 = \angle 8 \: \: \: \: \: \{vertically\:opposite\:angles \}$

$\bf\implies \:\angle 6 = 70\degree$

Also,

$\sf \: \angle 5 = \angle 7 \: \: \: \: \: \{vertically\:opposite\:angles \}$

$\bf\implies \:\angle 7 = 110\degree$

Hence, we have

$\bf\implies \:\angle 2 = \angle 4 = \angle 6 = \angle 8 = 70\degree$

and

$\bf\implies \:\angle 1 = \angle 3 = \angle 5 = \angle 7 = 110\degree$