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How do you figure this out?

How do you figure this out?-example-1
User Janovesk
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1 Answer

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Answer:

  • ∠g and ∠h are complementary angles
  • ∠g and ∠h are acute angles

Explanation:

Use the given information to determine what the angles can be.

g = 2x -90 . . . . given

g > 0 . . . . . . . . . given

2x -90 > 0

2x > 90 . . . . . add 90

x > 45 . . . . . . divide by 2

__

h = 180 -2x

h > 0

180 -2x > 0

180 > 2x

90 > x

__

The requirement that both angles be greater than zero puts limits on x:

45 < x < 90

We can put this back into the given relations for g and h:

g = 2x -90

x = (g +90)/2

45 < (g +90)/2 < 90 . . . . substitute for x

0 < g/2 < 45 . . . . . . . . . . subtract 45

0 < g < 90 . . . . . . . . . . . . g is an acute angle

Similarly, ...

h = 180 -2x

x = (180 -h)/2 = 90 -h/2

45 < (90 -h/2) < 90 . . . . substitute for x

-45 < -h/2 < 0 . . . . . . . . . subtract 90

90 > h > 0 . . . . . . . . . . . multiply by -2; h is an acute angle

__

We can add the angle measures to see if they are supplementary or complementary:

g + h = (2x -90) +(180 -2x)

g + h = 90 . . . . . simplify; the angles are complementary

__

The relevant observations are ...

  • ∠g and ∠h are complementary angles
  • ∠g and ∠h are acute angles
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