Chapter 12.1, Problem 47E

To determine

To find:the measurement of an exteriorand two interior angles.

Answer to Problem 47E

  $A,BD,F$ is true and $C\text{ and }E$ .

Explanation of Solution

Given:

  

Concept used:

Sum of any two nonadjacent interior angles is equal to the exterior angle.

Sum of the three 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:

  $\left(A\right)$ :

The third interior angle is $180-62-38={80}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $62+38=100.$

Which is true.

  $\left(B\right)$ :

Third interior angle is $180-57-24={99}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $57+24={81}^0$ .

Which is true.

  $\left(C\right)$ :

Third interior angle is $180-68-49={63}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $\begin{array}{l}68+49=117\ne 63.\\ 49+63=112\ne 68.\\ 68+63=132\ne 49.\end{array}$

So, it is not true.

  $\left(D\right)$ :

Third interior angle is $180-68-49={63}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $28+67={95}^0$ .

  $\left(E\right)$ :

Third interior angle is $180-78-68={34}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $\begin{array}{l}78+68=146\ne 34.\\ 78+34=112\ne 68.\\ 68+34=102\ne 78.\end{array}$

So, it is not true.

  $\left(F\right)$ :

Third interior angle is $180-101-48={31}^0.$

Sum of any two nonadjacent interior angles is equal to the exterior angle.

  $101+48={149}^0$ .

So, it is true.

Hence, $A,BD,F$ is true and $C\text{ and }E$ .