Answer:
The measure of the angle is 19.38°.
Step-by-step explanation:
An angle is a supplement of another angle when its sum equals 180 degrees. In this case:
[tex]\alpha + \beta = 180^{\circ}[/tex]
And according to the statement:
[tex]\beta = 7\cdot \alpha + 25^{\circ}[/tex]
Where:
[tex]\alpha[/tex] - Angle, measured in degrees.
[tex]\beta[/tex] - Supplement, measured in degrees.
The following system of equations is formed:
[tex]\alpha + \beta = 180^{\circ}[/tex]
[tex]7\cdot \alpha - \beta = -25^{\circ}[/tex]
The solution of the system is [tex]\alpha \approx 19.38^{\circ}[/tex] and [tex]\beta \approx 160.63^{\circ}[/tex]. And finally, the measure of the angle is 19.38°.
