Apartial proof was constructed given that mnop is a parallelogram. by the definition of a parallelogram, mn ∥ po and mp ∥ no. using mp as a transversal, ∠m and ∠p are same-side interior angles, so they are supplementary. using no as a transversal, ∠n and ∠o are same-side interior angles, so they are supplementary. using op as a transversal, ∠o and ∠p are same-side interior angles, so they are supplementary. therefore, and because they are supplements of the same angle. which statements should fill in the blanks in the last line of the proof?
∠m is supplementary to ∠n; ∠m is supplementary to ∠o
∠m is supplementary to ∠o; ∠n is supplementary to ∠p
∠m ≅ ∠p; ∠n ≅ ∠o
∠m ≅ ∠o; ∠n ≅ ∠p

Step-by-step explanation:

According to the problem

Which means,

And,

Therefore, the right answer is the last choice.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.