Answer :

To convert an angle from degrees to radians, we use the conversion factor [tex]\(\pi\)[/tex] radians [tex]\( = 180^\circ\)[/tex]. This means:

[tex]\[ 1^\circ = \frac{\pi}{180} \text{ radians} \][/tex]

Let's go through each conversion step by step.

### 1. [tex]\(40^\circ\)[/tex] to radians

First, we apply the conversion factor:

[tex]\[ 40^\circ \times \frac{\pi}{180} \][/tex]

Simplify the fraction:

[tex]\[ \frac{40\pi}{180} \][/tex]

Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 20:

[tex]\[ \frac{40\pi}{180} = \frac{2\pi}{9} \][/tex]

So, [tex]\(40^\circ\)[/tex] in radians is:

[tex]\[ 40^\circ = \frac{2\pi}{9} \][/tex]

### 2. [tex]\(-105^\circ\)[/tex] to radians

Similarly, apply the conversion factor:

[tex]\[ -105^\circ \times \frac{\pi}{180} \][/tex]

Simplify the fraction:

[tex]\[ \frac{-105\pi}{180} \][/tex]

Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 15:

[tex]\[ \frac{-105\pi}{180} = \frac{-7\pi}{12} \][/tex]

So, [tex]\(-105^\circ\)[/tex] in radians is:

[tex]\[ -105^\circ = \frac{-7\pi}{12} \][/tex]

### Final Answers

Thus, the measures converted to radians are:

1. [tex]\(40^\circ = \frac{2\pi}{9}\)[/tex]
2. [tex]\(-105^\circ = \frac{-7\pi}{12}\)[/tex]