Question

Geometry angles, please help. :)

Answer 1

Given :–

∠6 = 115°

To find :–

∠1, ∠2, ∠3, ∠4, ∠5, ∠7, ∠8

SoLuTiOn :–

As, we know that,

The two lines are parallel say L,S are the parallel and R is the transversal .

By the transversal properties

We know that,

∠1 = ∠4

∠2 = ∠3

∠5 = ∠8

∠6 = ∠7

Vertically opposite angles are equal

_______________..

∠1 + ∠2 = 180°

∠3 + ∠4 = 180°

∠5 + ∠6 = 180°

∠7 + ∠8 = 180°

Beacuse they forms linear pair

________________..

∠1 = ∠5

∠2 = ∠6

∠3 = ∠7

∠4 = ∠8

Corresponding angles are equal

_______________..

∠3 + ∠5 = 180°

∠4 + ∠6 = 180°

Co-interior angles sums is Supplementary

______________..

∠1 + ∠7 = 180°

∠2 + ∠8 = 180°

Co-exterior angles sum is Supplementary

________________..

∠3 = ∠6

∠4 = ∠5

Alternate interior angles are equal

________________..

∠1 = ∠8

∠2 = ∠7

Alternate exterior angles are equal

______________..

So, by using this information we can find the remaining angles.

∠6 = 115°

∠6 = ∠7 = 115°[Vertically opposite angles are equal]

∠5 + ∠6 = 180°[Linear pair]

∠5 + 115° = 180°

∠5 = 180°-115°

∠5 = 65°

∠5 = ∠8 =65° [Vertically opposite angles are equal]

∠1 = ∠5 = 65° [Corresponding angles are equal]

∠2 = ∠6= 115°[Corresponding angles are equal]

∠3 = ∠7 = 115° [Corresponding angles are equal]

∠4 = ∠8 = 65° [Corresponding angles are equal]

So,

∠1 = 65°

∠2 = 115°

∠3 = 115°

∠4 = 65°

∠5 = 65°

∠6 = 115°

∠7 = 115°

∠8 = 65°[tex][/tex]