Step 1: Convert the percentage abundances to fractional abundances. The fractional abundance is the percentage abundance divided by 100. For $^{35}\text{Cl}$: $75.4\% = \frac{75.4}{100} = 0.754$ For $^{37}\text{Cl}$: $24.6\% = \frac{24.6}{100} = 0.246$ Step 2: Use the formula for average atomic mass. The average atomic mass is calculated by summing the products of each isotope's mass and its fractional abundance. $$\text{Average atomic mass} = (\text{mass of isotope 1} \times \text{fractional abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{fractional abundance of isotope 2})$$ Step 3: Substitute the given values into the formula. We assume the isotopic masses are approximately equal to their mass numbers, i.e., $35$ amu for $^{35}\text{Cl}$ and $37$ amu for $^{37}\text{Cl}$. $$\text{Average atomic mass} = (35 \text{ amu} \times 0.754) + (37 \text{ amu} \times 0.246)$$ Step 4: Perform the multiplication and addition. $$\text{Average atomic mass} = 26.39 \text{ amu} + 9.102 \text{ amu}$$ $$\text{Average atomic mass} = 35.492 \text{ amu}$$ The average atomic mass of chlorine is $\boxed{\text{35.492 amu}}$.