Mathematics

The measure of an angle is four times the measure of its supplementary angle. Then the angles are __________.


ANSWER

$$36^o, 144^o$$


SOLUTION
Two angles are called to be supplementary if the summation of both angles is $$180^{\circ}$$.
say $$\angle A $$ and $$\angle B $$ are supplementary angles
$$\Rightarrow $$          $$\angle A $$ $$+$$ $$\angle B $$ $$=180^{\circ}$$
$$\because \angle A = 4\times \angle B$$        (Given in question)
so,  $$ 4\times \angle B$$ $$+$$ $$\angle B $$ $$=180^{\circ}$$
$$\Rightarrow $$            $$ 5\times \angle B$$   $$=180^{\circ}$$
$$\Rightarrow $$                   $$  \angle B$$   $$=36^{\circ}$$
Now, $$ \angle A = 4\times \angle B$$ 
$$\Rightarrow $$   $$  \angle A$$   $$=4\times36^{\circ}$$
$$\Rightarrow $$   $$  \angle A$$   $$=144^{\circ}$$
so these angles are $$36^{\circ}$$, $$144^{\circ}$$
Hence the option $$(A)$$ $$36^{\circ}$$, $$144^{\circ}$$ is correct.
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
Find the angle which is $$80^o$$ more than its complement
  • A. $$75$$
  • B. $$95$$
  • C. $$100$$
  • D. $$85$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q2 Subjective Medium
In the following diagram which three lines are perpendicular to line l? Show them symbolically:

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 23rd 09, 2020

View Answer
Q3 Subjective Medium
In the given figure:
If $$\angle AOB= \angle BOC=\angle COD=38^o$$; 
Find : reflex angle $$AOC$$ and reflex angle $$AOD$$ 

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Single Correct Medium
Angles which are both supplementary and vertically opposite are 
  • A. $$95^o , 85^o$$
  • B. $$100^o, 80^o$$
  • C. $$45^o, 45^o$$
  • D. $$90^o, 90^o$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 Single Correct Medium
In the given figure below points $$A, O$$, and $$C$$ lie on the same line. What is the sum of the measures of $$\angle AOD$$ and $$\angle DOC$$?
  • A. $$\displaystyle 90^{\circ}$$
  • B. $$\displaystyle 270^{\circ}$$
  • C. $$\displaystyle 360^{\circ}$$
  • D. $$\displaystyle 180^{\circ}$$

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer