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Difficulty:
25%
(medium)
Question Stats:
81% (01:35) correct
19%
(01:44)
wrong
based on 26
sessions
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Find the degree measure of an angle whose complement is 25% of its supplement. (Supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°).
(A) 48
(B) 60
(C) 75
(D) 120
(E) 150
(A) 48
(B) 60
(C) 75
(D) 120
(E) 150
26 Jul 2022, 18:40
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Find the degree measure of an angle whose complement is 25% of its supplement. (Supplementary angles are two angles that add up to 180°, whereas complementary angles are two angles that add up to 90°).
(A) 48
(B) 60
(C) 75
(D) 120
(E) 150
(A) 48
(B) 60
(C) 75
(D) 120
(E) 150
Let the angle be x degrees. Then, its complement is 90 - x degrees, and its supplement is 180 - x degrees. Since we want the former to be 25% = 1/4 of the latter, we can write:
\(\Rightarrow\) 90 - x = 1/4 * (180 - x)
\(\Rightarrow\) 90 - x = 45 - x/4
\(\Rightarrow\) 90 - 45 = x - x/4
\(\Rightarrow\) 45 = 3x/4
\(\Rightarrow\) x = 45 * 4/3 = 60
Alternate Solution:
We can test each answer choice. When we subtract the correct answer from 180, we should obtain four times the number we obtain when we subtract the angle from 90:
Answer choice A: We have 90 - 48 = 42 and 180 - 48 = 132. Since 132 is not equal to 4 * 42 = 168, answer choice A is not correct.
Answer choice B: We have 90 - 60 = 30 and 180 - 60 = 120. Since 120 is 4 * 30, answer choice B is correct.
Answer: B
