Chapter 12.1, Problem 34E

To determine

To find: the measurement of the given numbered angle.

Answer to Problem 34E

  $m\angle 6=140$ .

Explanation of Solution

Given:

  

Concept used:

If a triangle is a right triangle, so both acute angles are complementary.

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

Vertical opposite angles are always equal.

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

Calculation:

The given triangle is a right triangle, so both acute angles are complementary.

Angle $\angle 1$ is complementary to angle with measure ${40}^0$ .

This mean that:

  $\begin{array}{l}m\angle 1+40=90.\\ m\angle 1=50.\end{array}$

Since, vertical opposite angle are always equal.

  $m\angle 1=m\angle 3=50.$

Two angles are said to be complementary when sum of the two angles is ${90}^0$ .

  $\begin{array}{l}m\angle 3+m\angle 5=90.\\ 50+m\angle 5=90.\\ m\angle 5=40.\end{array}$

Two angles are said to supplementary when sum of the two angle is ${180}^0$ .

  $\begin{array}{l}m\angle 5+m\angle 6=180.\\ 40+m\angle 6=180.\\ m\angle 6=140.\end{array}$

Hence, $m\angle 6=140$ .