Question

If in the figure a||b and c||d, then name the angles that are congruent to (i) ∠1 (ii) ∠2.

Answer 1

Hi ,

It is given that a // b and c // d

<1 = <3 ( vertically opposite angles )

<1 = <5 ( corresponding angles )

<1 = <9 ( corresponding angles )

Also

<1 = <3 = <5 = <7 ;

<1 = <11 = <9 = <13 = <15

Similarly ,

<2 = <4 = <6 = <8

Also

<2 = <10 = <12 = <14 = <16

I hope this helps you.

: )

Answer 2

Answer:

(i) $\angle 1=\angle 3=\angle 5=\angle 7=\angle 9=\angle 11=\angle 13=\angle 15$

(ii) $\angle 2=\angle 4=\angle 6=\angle 8=\angle 10=\angle 12=\angle 14=\angle 16$

Step-by-step explanation:

It is given that a||b and c||d.

If a transversal line intersect two parallel lines, then

(i) Corresponding angles are congruent.

(ii) Alternative interior angles are congruent.

(iii) Alternative exterior angles are congruent.

From the given figure it is clear that

$\angle 1=\angle 5=\angle 9=\angle 13$       (Corresponding angles)

$\angle 2=\angle 6=\angle 10=\angle 14$       (Corresponding angles)

$\angle 3=\angle 7=\angle 11=\angle 15$       (Corresponding angles)

$\angle 4=\angle 8=\angle 12=\angle 16$       (Corresponding angles)

$\angle 1=\angle 7$       (Alternative exterior angles)

$\angle 2=\angle 8$       (Alternative exterior angles)

Using above equations we conclude that

$\angle 1=\angle 3=\angle 5=\angle 7=\angle 9=\angle 11=\angle 13=\angle 15$

$\angle 2=\angle 4=\angle 6=\angle 8=\angle 10=\angle 12=\angle 14=\angle 16$