Answer:
The measure of the two angles is 30° and 20°.
Step-by-step explanation:
The intern angles of a quadrilateral must add up to 360 degrees. Then, if the two given angles add up to 310°, then the two missing angles must add up to:
[tex]360\degree-310\degree=50\degree[/tex]Let be x and y our missing angles, then our first equation would be:
[tex]x+y=50[/tex]Since we also know the ratio between these angles, the second equation for the system would be:
[tex]\begin{gathered} \frac{x}{y}=\frac{2}{3} \\ x=\frac{2}{3}y \end{gathered}[/tex]Now, plug the second equation of the system into the first one to solve the system:
[tex]\frac{2}{3}y+y=50[/tex]Solve for y.
[tex]\begin{gathered} \frac{5}{3}y=50 \\ y=\frac{50\cdot3}{5} \\ y=30\text{ degrees} \end{gathered}[/tex]One of the angles measures 30 degrees, then the other one:
[tex]\begin{gathered} x=50-30 \\ x=20\text{ degrees} \end{gathered}[/tex]The measure of the two angles is 30° and 20°.
