Mathematics

An angle is such that the ratio between its complementary and supplementary angles is $$1:4$$. Then the angle measure is?


ANSWER

$$60^o$$


SOLUTION
Let the required angle be $$x$$

Then according to the question,
$$\Rightarrow$$  $$\dfrac{90^o-x}{180^o-x}=\dfrac{1}{4}$$

$$\Rightarrow$$  $$4(90^o-x)=180^o-x$$

$$\Rightarrow$$  $$360^o-4x=180^o-x$$

$$\Rightarrow$$  $$360^o-180^o=-x+4x$$

$$\Rightarrow$$  $$180^o=3x$$

$$\Rightarrow$$  $$x=\dfrac{180^o}{3}$$

$$\therefore$$  $$x=60^o$$
$$\therefore$$   The required angle is $$60^o.$$
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Single Correct Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
A bicycle wheel makes four and half turns, then the number of right angles through which it turns is ________.
  • A. 16
  • B. 20
  • C. 8
  • D. 18

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Single Correct Medium
In the given figure, $$\displaystyle \angle 1={ 70 }^{ o }$$. Find $$180^o-\displaystyle 2\angle x$$.
  • A. $$\displaystyle { 50 }^{ o }$$
  • B. $$\displaystyle { 45 }^{ o }$$
  • C. $$\displaystyle { 60 }^{ o }$$
  • D. $$\displaystyle { 40 }^{ o }$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q3 TRUE/FALSE Medium
Which of the following statements are true (T) and which are false (F)?
If two adjacent angles are equal, then each angle measures $$90^{\circ}$$.
  • A. True
  • B. False

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Single Correct Medium
In the given figure, magnitude of angles are ________ .
  • A. $${ 40 }^{ o },{ 120 }^{ o }$$
  • B. $${ 30 }^{ o },{ 90 }^{ o }$$
  • C. $${ 50 }^{ o },{ 150 }^{ o }$$
  • D. $${ 45 }^{ o },{ 135 }^{ o }$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 23rd 09, 2020

View Answer
Q5 Subjective Medium
What is an Obtuse Angle ?

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer