Question

If two supplementary angles are in the ratio 1:3, then the larger of two angles is

Answer 1

Answer:

135°

Step-by-step explanation:

the ratio of two supplementary angle is 1:3

if the small angle is A°, then the other is 3A°

We know addition of two supplementary angle is 180°

Then A+3A=180 ⇒ 4A = 180 ⇒ A=45

Hence the larger angel is 3A° = 3×45° = 135°

Answer 2

To find : larger of supplementary angles .

Given : two supplementary angles are in the ratio $1:3$ .

Solution :

• Supplementary angles are the angles whose measure adds up to $180$°.

        i.e. ∠A +∠B = $180$°

• We are given that two supplementary angles are in the ratio $1:3$ .
• Let , $1x$ and $3x$ be two angles in ratio .
• Then according to given data we write given condition as ,
• $1x + 3x = 180$

               $4x =180 \\x = \frac{180 }{4}\\\x = 45$

• Now , supplementary angles are , $1x = 1\times 45 =45$°

                                                                 $3x = 3\times 45 = 135$°  

Hence , larger of two angles is $135$° .