Find the Angle Relationship: Determining α When β = 100°

To solve this problem, we need to understand the relationship between the angles $\alpha$ and $\beta$ given in the diagram.

Step 1: Determine the relationship between $\alpha$ and $\beta$. The angles $\alpha$ and $\beta$ appear to be supplementary, forming a straight line. Hence, their sum is $180^\circ$.

Step 2: Use the given information to calculate $\alpha$. Given $\beta = 100^\circ$, we have:

$\alpha = 180^\circ - \beta = 180^\circ - 100^\circ = 80^\circ.$

Step 3: Calculate the ratio $\alpha:\beta$.

$\text{Ratio of } \alpha \text{ to } \beta = \frac{\alpha}{\beta} = \frac{80}{100} = \frac{4}{5}.$

Step 4: Express the ratio in the required form, which is a multiple-choice problem comparing given choices:

Therefore, the relationship between angle $\alpha$ and $\beta$ according to the drawing is 4:5.