When two parallel lines are intersected by a transversal, which pair of angles are always supplementary? select all that apply.

a.
corresponding angles

b.
vertical angles

c.
same-side interior angles

d.
alternate interior angles

e.
alternate exterior angles

f.
same-side exterior angles

Same-Side Interior Angles and Same-Side Exterior Angles

C and F

Step-by-step explanation:

We are given that two parallel lines are intersected by  a transversal.

We have to find pair of supplementary  angles.

Supplementary angle: Two  angles whose sum is equal to 180 degrees are called supplementary angles.

A.

Corresponding angles

It is not necessary that sum of corresponding angles is always equal to 180 degrees.Therefore, pair of angles are not always supplementary.

So, it is true.

B.Vertical angles

It is not necessary that sum of vertical angles is  always  equal to 180 degrees.Therefore, pair of angles are not always supplementary.

So, it is not true.

C.Same- side interior angles.

We know that  sum of same side interior angles is  always equal to 180 degrees.Therefore, they are always supplementary.

So, it is true.

D.Alternate interior angles

It is not necessary that sum of Alternate  interior angles is  always equal to 180 degrees.Therefore, pair of angles are not always supplementary.

So, it is not true.

E.Alternate exterior angles

It is not necessary that sum of Alternate  exterior angles is  always  equal to 180 degrees.Therefore, pair of angles are not always supplementary.

So, it is not true.

F.Same side exterior angles

We know that  sum of same side exterior angles is  always equal to 180 degrees.Therefore, they are always supplementary.

C and F

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.