Question

The measure of the supplement of an angle is 25 degrees more than 7 times the measure of the angle. To the nearest hundredth, what is the measure of the angle?

Answer 1

The measure of the angle is 19.38°.

Explanation:

An angle is a supplement of another angle when its sum equals 180 degrees. In this case:

`\alpha + \beta = 180^(\circ)`

And according to the statement:

`\beta = 7\cdot \alpha + 25^(\circ)`

Where:

`\alpha` - Angle, measured in degrees.

`\beta` - Supplement, measured in degrees.

The following system of equations is formed:

`\alpha + \beta = 180^(\circ)`

`7\cdot \alpha - \beta = -25^(\circ)`

The solution of the system is
`\alpha \approx 19.38^(\circ)` and
`\beta \approx 160.63^(\circ)`. And finally, the measure of the angle is 19.38°.