Chapter 6.1, Problem 2WE

a.

To determine

To state: whether the other statement can be deduced from the given statement

Answer to Problem 2WE

No

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle 1=m\angle 2$

  

If point B lies in the interior of $\angle AOC$ it cannot be concluded that $m\angle 1=m\angle 2$ .

So,

Answer is NO

b.

To determine

To state: whether the other statement can be deduced from the given statement

Answer to Problem 2WE

Yes

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle AOC=m\angle 1+m\angle 2$

  

Point B lies in the interior of $\angle AOC$

  $\begin{array}{c}m\angle AOC=m\angle AOB+m\angle COB\\ =m\angle 1+m\angle 2\end{array}$

So,

Answer is Yes

c.

To determine

To state: The other statement can be deduced from the given statement

Answer to Problem 2WE

Yes

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle AOC>m\angle 1$

  

Point B lies in the interior of $\angle AOC$

  $\begin{array}{c}m\angle AOC=m\angle AOB+m\angle COB\\ =m\angle 1+m\angle 2\end{array}$

So,

  $m\angle AOC>m\angle 1$

Answer is Yes

d.

To determine

To state: whether the other statement can be deduced from the given statement

Answer to Problem 2WE

Yes

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle AOC>m\angle 2$

  

Point B lies in the interior of $\angle AOC$

  $\begin{array}{c}m\angle AOC=m\angle AOB+m\angle COB\\ =m\angle 1+m\angle 2\end{array}$

So,

  $m\angle AOC>m\angle 2$

Answer is Yes

e.

To determine

To state: whether the other statement can be deduced from the given statement

Answer to Problem 2WE

No

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle 1>m\angle 2$

  

Point B lies in the interior of $\angle AOC$

No, it cannot be deduced that $m\angle 1>m\angle 2$

f.

To determine

To state: whether the other statement can be deduced from the given statement

Answer to Problem 2WE

No

Explanation of Solution

Given information: Point B lies in the interior of $\angle AOC$ . $m\angle AOC>90°$

  

Point B lies in the interior of $\angle AOC$

No, it cannot be deduced that $m\angle AOC>90°$