Question

Find the missing angle measure in each triangle. classify if these triangles are acute obtuse or right explain why

Answer 1

The addition of the three interior angles of a triangle is equal to 180 degrees.

Considering triangle ABC, we have:

`m\angle A+m\angle B+m\angle C=180\degree`

Angle A measures 50° and angle B measures 75°. Substituting these values in the above equation and solving for the measure of angle C:

`\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}`

Triangle ABC is an acute triangle because its three angles are acute (less than 90°).

Considering triangle DEF, we have:

`m\angle D+m\angle E+m\angle F=180\degree`

Angle D measures 60° and angle F measures 30°. Substituting these values in the above equation and solving for the measure of angle E:

`\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}`

Triangle DEF is a right triangle because one of its angles is right (it measures 90°)

Considering triangle HKJ, we have:

`m\angle H+m\angle K+m\angle J=180\degree`

Angle K measures 45° and angle J measures 30°. Substituting these values in the above equation and solving for the measure of angle H:

`\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}`

Triangle HKJ is an obtuse triangle because one of its angles is obtuse (greater than 90°)