Question

The larger of two supplementary angles exceeds 7 times the smaller by 4 degrees. What is the measure of the larger angle?

Answer 1

The measure of larger angle`=158^o`

Explanation:

Let's take:
Larger Angle`=L`
Smaller Angle`=S`

If these two angles are supplementary, it means:
`L+S=180^o ..........(i)`

It is given `L` exceeds 7 times of `S` by 4 degrees, i.e.
`L=(7xxS)+4=7S+4`

Now put the above value of `L` in `eq.(i)`
`(7S+4)+S=180^o`
=> `8S+4=180`
=> `8S=180-4`
=> `8S=176`
=> `S=176-:8`
=> `S=22^o`

Now we can find the value of `L` from `eq.(i)` as:
`L=180^o-S=180^o-22^o=158^o`