1.given a∥b , and c is not parallel to a or b, which statements must be true? select each correct answer. m∠7=m∠11 m∠5=m∠12 m∠4=m∠5 m∠1=m∠5 2.in the figure, ab¯¯¯¯¯∥cd¯¯¯¯¯ and m∠4=85°. what is m∠5? enter your answer in the box.

1. We have been given that a∥b , and c is neither parallel to a nor b.

Let us see which of our given options are correct.

A. m∠7 can not be equal to m∠11  as line c is not parallel to line a.

B. m∠5 can not be equal to m∠12 as line c is not parallel to line b.

C. By alternate interior angles m∠4=m∠5  as ∠4 is inside line a and ∠5 is inside line b. Both angles are on the opposite sides of transversal.  

D. Since we know that corresponding angles are congruent. We can see that ∠5 corresponds to ∠1, therefore, m∠1=m∠5.

Therefore, Option C and D are correct choices.

2. We have been given that  AB∥CD and m∠4=85°. We are asked to find measure of ∠5.

Since we know that same side interior angles are supplementary. In our figure we can see that  ∠4 and ∠5 are same side interior angles.

Therefore, measure of ∠5 will be 95 degrees.  

2,160 π

step-by-step explanation:

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734