11. the two complementary angles are in the ratio 1/5 find the measures of the angles.

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

  Is there an error in this question or solution?

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

  Is there an error in this question or solution?

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

  Is there an error in this question or solution?

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

  Is there an error in this question or solution?

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

  Is there an error in this question or solution?

Answer (Detailed Solution Below)

Option 1 : 60° 

Free

100 Qs. 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. 

Ace your Geometry preparations for Lines and Angles with us and master Quantitative Aptitude for your exams. Learn today!

India’s #1 Learning Platform

Start Complete Exam Preparation

Video Lessons & PDF Notes

Get Started for Free Download App

Trusted by 2,94,96,332+ Students