Question

In the figure,
=m∠14x°
and
=m∠2−x5°
.

1
2
(a)Write an equation to find
x
. Make sure you use an "
=
" sign in your answer.

Equation:
(b)Find the degree measure of each angle.

=m∠1
°
=m∠2
°

Answer 1

To solve for \( x \) with the given angles \( m\angle 1 = 14x^\circ \) and \( m\angle 2 = 2 - \frac{x}{5} \) degrees, we'll first write the equation based on the relationship between these angles.

### (a) Write an Equation

Since the problem does not specify whether the angles are equal or some other relationship, I'll assume that \( m\angle 1 \) and \( m\angle 2 \) are equal. Thus, we can write:

\[
14x = 2 - \frac{x}{5}
\]

### (b) Solve for \( x \) and Find Each Angle

To solve for \( x \):

1. Eliminate the fraction by multiplying every term by 5 to simplify:
\[
5(14x) = 5\left(2 - \frac{x}{5}\right)
\]
This results in:
\[
70x = 10 - x
\]

2. Now, add \( x \) to both sides:
\[
70x + x = 10
\]
This simplifies to:
\[
71x = 10
\]

3. Now, divide both sides by 71:
\[
x = \frac{10}{71}
\]

Now we can find the degree measure of each angle.

1. For \( m\angle 1 \):
\[
m\angle 1 = 14x = 14 \times \frac{10}{71} = \frac{140}{71} \approx 1.97^\circ
\]

2. For \( m\angle 2 \):
\[
m\angle 2 = 2 - \frac{x}{5}
\]
First calculate \( \frac{x}{5} \):
\[
\frac{x}{5} = \frac{10/71}{5} = \frac{10}{355} = \frac{2}{71}
\]
Thus,
\[
m\angle 2 = 2 - \frac{2}{71} = \frac{142}{71} - \frac{2}{71} = \frac{140}{71} \approx 1.97^\circ
\]

### Final Answers

Thus, we have:

1. **Equation**: \( 14x = 2 - \frac{x}{5} \)
2. **Degree measures**:
\[
m\angle 1 \approx 1.97^\circ
\]
\[
m\angle 2 \approx 1.97^\circ
\]

Both angles will have the same measure, as expected from our equation.