Fill in the blanks for the letters with the missing reason in the flow proof

m<5=40.

a. Given.

m<2 = 140 degrees

b. given

<5 and <2 are supplementary angles

c. Sum of <5 and <2 is 180 degree.

< 5 and <2 are same side-interior angles

d. Same side-interior angles are called Consecutive Interior Angles.

a||b

e. When Consecutive Interior Angles are supplementary (sum 180) the linear are parallel.

27

Step-by-step explanation:

note that tanx cotx = tanx × = 1

Given

tanx - cotx = 5 ( square both sides )

(tanx - cotx)² = 5² = 25 ← expand left side using FOIL

tan²x - 2tanxcotx + cot²x = 25

tan²x - 2 + cot²x = 25 ( add 2 to both sides )

tan²x + cot²x = 27