Question

Find the measures of the supplementary angles if:

Their difference is equal to 35°

Answer 1

sum of supplementary = 180
180 - 35 = 145

145/2 = 72.5

so
one angle = 72.5
and
its supplement = 72.5 + 35 = 107.5

Answer 2

The measures of the supplementary angles is 72.5° and 107.5°

Explanation:

Given : The difference of the two angles is equal to 35°

To Find :Find the measures of the supplementary angles

Solution:

Let the angle be x

Supplementary angles : A pair of angle whose sum is 180° .

So, Supplement of x° is (180-x)°

Now we are given that Their difference is equal to 35°

`\Rightarrow x-(180-x)=35^(\circ)`

`\Rightarrow x-180+x=35^(\circ)`

`\Rightarrow 2x=35+180`

`\Rightarrow 2x=215`

`\Rightarrow x=(215)/(2)`

`\Rightarrow x=107.5`

Supplement of 107.5°= (180-107.5)° = 72.5°

The measures of the supplementary angles is 72.5° and 107.5°