Chapter 12.1, Problem 11E

To determine

To find: the classification of the triangle by its given angle and calculate the angle $m\angle 1$ .

Answer to Problem 11E

  $m\angle 1={71}^0$ .

Explanation of Solution

Given:

  

Concept used:

Sum of the three interior angles of triangle is always ${180}^0$ .

If the triangle is right triangle then other two angles other than ${90}^0$ will be less than ${90}^0$ .

Calculation:

According to the triangle sum theory:

The sum of the three interior angles of triangle is always ${180}^0$ .

If the triangle has three acute angles:

  $\left({78}^0,{31}^0,m\angle 1\right)$

Sum of three angle $={180}^0$ .

  $\begin{array}{l}{78}^0+{31}^0+m\angle 1={180}^0.\\ {109}^0+m\angle 1={180}^0.\\ m\angle 1={71}^0.\end{array}$

Hence, the angle of $m\angle 1={71}^0$ .