Question

Two angles are supplementary. When the smaller is increased by 30°, it becomes 20° less than its new supplement. Find the original angles.?

Answer 1

The two angles are `65^@` and `155^@`.

Explanation:

You can create a system of equations by "translating" the two English statements to math:

`stackrel(m/_1+m/_2) overbrace"Two angles"" "stackrel(=)overbrace"are"" " stackrel(180^@)overbrace"supplementary"`

`stackrel(m/_1+30^@)overbrace"When the smaller is increased by 30º,"" "stackrel(=)overbrace"it becomes"" "stackrel(180^@-m/_1-20^@)overbrace"20º less than its new supplement"`

Here's our system of equations now:

`{ (m/_1+m/_2=180^@, qquad(1)), (m/_1+30^@=180^@-m/_1-20^@, qquad(2)) :}`

Simplifying equation `(2)`:

`m/_1+30^@=180^@-m/_1-20^@`

`m/_1+50^@=180^@-m/_1`

`2m/_1+50^@=180^@`

`2m/_1=130^@`

`m/_1=65^@`

We can now use equation `(1)` to solve for the other angle measure:

`m/_1+m/_2=180^@`

`65^@+m/_2=180^@`

`m/_2=115^@`

The two original angles' measures are `65^@` and `155^@`.