Question 8 Revision Exercise
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Answer:
Solution: Ratio between two supplementary angles are= 7:5
Sum of ratios = 7+5=12
But sum of supplementary angles= 180°
First angle= 180° x \frac{7}{12}= 15° x 7=105°
and second angle = \frac{180\times5}{12}= 15 x 15= 75°
Two supplementary angles are 105° and 75°
Video transcript
"Hello, welcome to lido today we're going to see a question that is to supplementary angles and the ratio seven is to find find the angles so they are in the ratio of survival. Where is to find we're going to find the tangle it's to it. So first we need to find out what is the supplementary angles when supplementary made? Hello, welcome to your new home at clay get going to see a question that is to supplementary angles and the ratio 7 is to find find the angles. So they are in the ratio of surveys to find. We're going to find the tangle. It's to it. So first we need to find out what is the supplement trying to spend supplementary means the addition of the triangle is going to be 180 degrees. Supplementary Addition of two angles is 180 degrees. So it is given that it is a ratio. So very strike two angles and ratios on it when you're going to find the angle so should take as 7x plus Phi x equal to 180. Okay, so then what to do next so on X by X is 2x squared to 180. So x equals to 180 by 2 L is 180 by 2 L and take it out and do the division partner of first or 80 divided by 12 kill one jar 12. People fighter 60 so it will be 15 x so x value equals 215. So now put this value x value in this each terms and find out the each angle. So 7 into X. This is the first angle X so server into 15. So answer will be. 105 and then the other angle is Fi L 2X. Clean 215 Pfizer 75, so on the server 105 n 75 I hope you understand this video and thanks for watching this video. "
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100 Questions 100 Marks 60 Mins
Given:
Ratio of two complementary angles is 1 : 5
Concept used:
Sum of two complementary angles is 90°.
Calculations:
Let the two angles be 1x and 5x.
Sum of two complementary angles is 90°.
⇒ (1x + 5x) = 90°
⇒ x = 15°
⇒ (5x - x) = 60°
∴ The difference between two complementary angles is 60°.
Additional Information
Two angles are called complementary when their measures add to 90 degrees.
Two angles are called supplementary when their measures add up to 180 degrees.
Let's discuss the concepts related to Geometry and Lines and Angles. Explore more from Quantitative Aptitude here. Learn now!
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If two complementary angles are in the ratio 1 : 5, find them.
Two complementary angles are in the ratio = 1 : 5
Let these angles be x and 5x
∴ x + 5x = 90°
⇒ 6x = 90°
⇒ x = `(90°)/6` = 15°
∴ Angles will be 15° and 15°× 5 = 75°
Concept: Concept for Pairs of Angles
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Page 2
If two supplementary angles are in the ratio 2 : 7, find them.
Ratio between two supplementary angles = 2 : 7
Let the angles be 2x and 7x
∴ 2x + 7x = 180°
⇒ 9x = 180°
⇒ x = `(180°)/9` = 20°
∴ First Angle is 2x = 2 × 20° = 40°
Second Angle is 7x = 7 × 20° = 140°
Concept: Concept for Pairs of Angles
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Page 3
Three angles which add up to 180° are in the ratio 2 : 3 : 7. Find them.
Ratio of three angles = 2 : 3 : 7
Let first angle be = 2x
second angle = 3x
and third angle = 7x
∴ 2x + 3x + 7x = 180°
⇒ 12x = 180°
⇒ x = `(180°)/2` = 15°
∴ First angle = 2x = 2 × 15° = 30°
second angle = 3x = 3 × 15° = 45°
and third angle = 7x = 7 × 15° = 105°
Hence, the angles are 30°, 45° and 105°
Concept: Concept for Pairs of Angles
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Page 4
20% of an angle is the supplement of 60°. Find the angle.
Let the given angle be x
then 20% of x + 60° = 180°
⇒ 20% of x = 180°− 60° = 120°
⇒ `20/100xx"x"` = 120°
⇒ x =`(120xx100)/20`
⇒ x = 600°
Hence x = 600°
Concept: Concept for Pairs of Angles
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Page 5
10% of x° is the complement of 40% of 2x°. Find x
∵ 10% of x° is the complement of 40% of 2x°
∴ 10% of x° + 40% of 2x° = 90°
⇒ `10/100"x"+40/100xx2"x"=90°`
⇒ `(10"x")/100+(80"x")/100=90°`
⇒ `(90"x")/100` = 90°
∴ x = `(90xx100)/90`= 100°
Hence x = 100°
Concept: Concept for Pairs of Angles
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