Angels ABC and DEF are supplementary angles. The measure of angle ABC, in degrees, is given by the expression 2x + 10. The measure of angle DEF, in degrees, is given by the expression 3x - 15. What is the value of x?

Which pair of angles are vertical angles? ∠1 and ∠4 ∠1 and ∠2 ∠2 and ∠4 ∠2 and ∠3

Jeffery conducted a survey in his school and found that 30 of the 50 eighth grade students' favorite subject is mathematics. based on the results, jeffery concluded that out of the 200 students in his school, 120 students' favorite subject is mathematics. select the statement that is true about jeffery's conclusion. a. jeffery's conclusion is not valid because the sample was biased since only 200 students were surveyed. b. jeffery's conclusion is valid because the sample was random since all of the students were eighth grade students. c. jeffery's conclusion is valid because the sample was random. d. jeffery's conclusion is not valid because the sample was biased since all of the students were eighth grade students.

Which of the following are accepted without proof in a logical system? check all that apply.