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Angle A measures r degrees. The complement of angle A measures 90-r de
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25 Oct 2022, 07:43
25 Oct 2022, 07:43
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Angle A measures r degrees. The complement of angle A measures 90-r degrees, and the supplement of angle A measures 180-r degrees. If the measure of angle A is greater than the measure of its complement and less than one-half the measure of its supplement, which of the following gives all possible values of r?
A 0 < r < 45
B 45 < r < 60
C 60 < r < 90
D 90 < r < 180
E 180 < r < 270
A 0 < r < 45
B 45 < r < 60
C 60 < r < 90
D 90 < r < 180
E 180 < r < 270
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Re: Angle A measures r degrees. The complement of angle A measures 90-r de
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25 Oct 2022, 08:41
25 Oct 2022, 08:41
1
Given that the measure of angle A is greater than the measure of its complement and less than one-half the measure of its supplement and we need to find which of the following gives all possible values of r
Complement of A < A < \(\frac{1}{2}\) Supplement of A
90 - r < r < \(\frac{1}{2}\) * (180 - r)
Solving Left hand side of the equation we get
90 - r < r
=> r + r > 90
=> 2r > 90
=> r > \(\frac{90}{2}\)
=> r > 45 ...(1)
Solving right hand side of the equation we get
r < \(\frac{1}{2}\) * (180 - r)
Multiplying both the sides by 2 we get
2r < 180 - r
=> 2r + r < 180
=> 3r < 180
=> r < \(\frac{180}{3}\)
=> r < 60 ...(2)
From (1) and (2) we get
45 < r < 60
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Inequality Problems
Complement of A < A < \(\frac{1}{2}\) Supplement of A
90 - r < r < \(\frac{1}{2}\) * (180 - r)
Solving Left hand side of the equation we get
90 - r < r
=> r + r > 90
=> 2r > 90
=> r > \(\frac{90}{2}\)
=> r > 45 ...(1)
Solving right hand side of the equation we get
r < \(\frac{1}{2}\) * (180 - r)
Multiplying both the sides by 2 we get
2r < 180 - r
=> 2r + r < 180
=> 3r < 180
=> r < \(\frac{180}{3}\)
=> r < 60 ...(2)
From (1) and (2) we get
45 < r < 60
So, Answer will be B
Hope it helps!
Watch the following video to learn How to Solve Inequality Problems
Re: Angle A measures r degrees. The complement of angle A measures 90-r de
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16 Apr 2024, 09:47
16 Apr 2024, 09:47
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