Question

Two supplementary angles differ by 20°. Find the angles. ​

Answer 1

`\text{Method 1:}\\\text{Let the two supplementary angles be }x\text{ and }y.\text{ Let }x\text{ be the small angle and }y\\\text{be the large angle.}\\\text{According to the question,}\\x=y-20^o.......(1)\\\text{Since }x\text{ and }y\text{ are supplementary angles,}\\x+y=180^o..........(2)\\\text{Substituting value of }x\text{ from equation(1) in (2),}\\y-20^o+y=180^o\\\text{or, }2y=200^o\\\text{or, }y=100^o\\\text{Equation (1) becomes}\\x=100^o-20^o=80^o\\\text{So the angles are }80^o\text{ and }100^o.`

`\text{Method 2:}\\\text{Let the two angles be }x\text{ and }x+20^o.\\\text{Since they are supplementary,}\\x+x+20^o=180^o\\\text{or, }2x=160^o\\\text{or, }x=80^o\\\text{So the other angle = }x+20^o=80^o+20^o=100^o`

`\text{Method 3:}\\\text{Let the two supplementary angles be }x\text{ and }180^o-x.\text{ Let }x\text{ be the small angle}\\\text{and }180^o-x\text{ be the large angle.}\\\text{According to the question,}\\x=(180^o-x)-20^o\\\text{or, }2x=180^o-20^o=160^o\\\text{or, }x=80^o\\\text{So the other angle is }180^o-x=180^o-80^o=100^o`