UGC NET Exam > UGC NET Questions > If the complement of an angle x is equal to t...
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If the complement of an angle x is equal to the supplement of angle 4x and the supplement of an angle y is 4 times its complement, then what is the value of (x + y) ?
- a)80°
- b)90°
- c)100°
- d)120°
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If the complement of an angle x is equal to the supplement of angle 4x...
Given Information:
The complement of angle x is equal to the supplement of angle 4x.
The supplement of angle y is 4 times its complement.
Let's find the values of x and y:
1. Complement of angle x = 90 - x
Supplement of angle 4x = 180 - 4x
According to the given information:
90 - x = 180 - 4x
90 + 3x = 180
3x = 90
x = 30
2. Complement of angle y = 90 - y
Supplement of angle y = 180 - y
According to the given information:
180 - y = 4(90 - y)
180 - y = 360 - 4y
3y = 180
y = 60
Now find x + y:
x + y = 30 + 60
x + y = 90
Therefore, the value of (x + y) is 90°. Hence, the correct answer is option B.
The complement of angle x is equal to the supplement of angle 4x.
The supplement of angle y is 4 times its complement.
Let's find the values of x and y:
1. Complement of angle x = 90 - x
Supplement of angle 4x = 180 - 4x
According to the given information:
90 - x = 180 - 4x
90 + 3x = 180
3x = 90
x = 30
2. Complement of angle y = 90 - y
Supplement of angle y = 180 - y
According to the given information:
180 - y = 4(90 - y)
180 - y = 360 - 4y
3y = 180
y = 60
Now find x + y:
x + y = 30 + 60
x + y = 90
Therefore, the value of (x + y) is 90°. Hence, the correct answer is option B.
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Community Answer
If the complement of an angle x is equal to the supplement of angle 4x...
Concept Used :
θ1 + θ2 = 90° [Complementry angle]
θ1 + θ2 = 180° [Supplementry angle]
Calculation :
According to question,
⇒ 90° - x = 180° - 4x --------(1)
⇒ 180° - y = 4(90° - y) ------------(2)
On solving eq (1) and eq (2) :
⇒ 3x = 90°
⇒ x = 30°
⇒ 3y = 180°
⇒ y = 60°
⇒ x + y = 60° + 30° = 90°
∴ The correct answer is 90°.
θ1 + θ2 = 90° [Complementry angle]
θ1 + θ2 = 180° [Supplementry angle]
Calculation :
According to question,
⇒ 90° - x = 180° - 4x --------(1)
⇒ 180° - y = 4(90° - y) ------------(2)
On solving eq (1) and eq (2) :
⇒ 3x = 90°
⇒ x = 30°
⇒ 3y = 180°
⇒ y = 60°
⇒ x + y = 60° + 30° = 90°
∴ The correct answer is 90°.
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If the complement of an angle x is equal to the supplement of angle 4x and the supplement of an angle y is 4 times its complement, then what is the value of (x + y) ?a)80°b)90°c)100°d)120°Correct answer is option 'B'. Can you explain this answer?
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