Question

Please help. I will medal for a quick answer.

Write an inequality and solve.

1. Find the angles whose supplements measure more than three times the angle and whose complements measure less than twice the angle.

Answer 1

Let x be the angle.
180 - x is the supplement because supplementary angles sum to 180

supplements measure more than three times the angle

180 - x > 3*x

Answer 2

Let x be the angle.
90 - x is the complement because complementary angles sum to 90

complements measure less than twice the angle

90 - x < 2x

Answer 3

180 - x > 3*x

Add x to both sides

180 > 4x

45 > x

x < 45

Answer 4

90 - x < 2x

Add x to both sides

90 < 3x

30 < x

Answer 5

Thank you so much! :)

Answer 6

Combing these:

x < 45 and 30 < x gives the compound inequality:

30 < x < 45 <----

Answer 7

Thank you so much! :)

Answer 8

You are welcome.