Help needed desperately

80° , 100°, 80°

Step-by-step explanation:

∠ 1 and ∠ 2 form a straight line and sum to 180° , then

2x + 40 + 2y + 40 = 180

2x + 2y + 80 = 180 ( subtract 80 from both sides )

2x + 2y = 100 → (1)

∠ 1 and ∠ 3 are vertical angles and are congruent , then

2x + 40 = x + 2y ( subtract x from both sides )

x + 40 = 2y ( subtract 40 from both sides )

x = 2y - 40 → (2)

Substitute x = 2y - 40 into (1)

2(2y - 40) + 2y = 100

4y - 80 + 2y = 100

6y - 80 = 100 ( add 80 to both sides )

6y = 180 ( divide both sides by 6 )

y = 30

Substitute y = 30 into (2)

x = 2(30) - 40 = 60 - 40 = 20

Thus x = 20 and y = 30

Then

∠ 1 = 2x + 40 = 2(20) + 40 = 40 + 40 = 80°

∠ 2 = 2y + 40 = 2(30) + 40 = 60 + 40 = 100°

∠3 = x + 2y = 20 + 2(30) = 20 + 60 = 80°

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .