Question

8. An angle is 1/4 of its supplement.What is its magnitude?

Answer 1

$\large \star \blue {Question} \star$ :- An angle is $\dfrac{1}{4}$ of its supplement. What is its magnitude?


$\large \star \purple {Answer} \star$ :-


Let the angle be x

$\dfrac{1}{4}$ of x = $\dfrac{1}{4}$x

We know that, supplementary angles add upto 180°


According to the question,

x = $\dfrac{1}{4}$ × 180 - x

4x = 1 × 180 - x

4x = 180 - x

4x - x = 180

3x = 180

x = $\dfrac{180}{3}$

x = 60



$\therefore{}$ $\pink {The \: measure \: of \: angle \: is \: 60°}$

Answer 2

Answer:

36

Step-by-step explanation:

let the angle be x

the supplement becomes 180-x

but according to question

x=(180-x)/4

180-x+x=180

180-x+(180-x)/4=180

(720-4x+180-x)/4=180

900-5x=720

5x=180

x=180/5

x=36