The addition of the three interior angles of a triangle is equal to 180 degrees.
Considering triangle ABC, we have:
[tex]m\angle A+m\angle B+m\angle C=180\degree[/tex]Angle A measures 50° and angle B measures 75°. Substituting these values in the above equation and solving for the measure of angle C:
[tex]\begin{gathered} 50\degree+75\degree+m\angle C=180\degree \\ m\angle C=180\degree-50\degree-75\degree \\ m\angle C=55\degree \end{gathered}[/tex]Triangle ABC is an acute triangle because its three angles are acute (less than 90°).
Considering triangle DEF, we have:
[tex]m\angle D+m\angle E+m\angle F=180\degree[/tex]Angle D measures 60° and angle F measures 30°. Substituting these values in the above equation and solving for the measure of angle E:
[tex]\begin{gathered} 60\degree+m\angle E+30\degree=180\degree \\ m\angle E=180\degree-60\degree-30\degree \\ m\angle E=90\degree \end{gathered}[/tex]Triangle DEF is a right triangle because one of its angles is right (it measures 90°)
Considering triangle HKJ, we have:
[tex]m\angle H+m\angle K+m\angle J=180\degree[/tex]Angle K measures 45° and angle J measures 30°. Substituting these values in the above equation and solving for the measure of angle H:
[tex]\begin{gathered} m\angle H+45\degree+30\degree=180\degree \\ m\angle H=180\degree-45\degree-30\degree \\ m\angle H=105\degree \end{gathered}[/tex]Triangle HKJ is an obtuse triangle because one of its angles is obtuse (greater than 90°)
