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In this problem, the diagram shows a straight line \( AB \) with point \( D \) on it, and a vertical line \( C \) perpendicular to \( AB \) at \( D \). The angles \( \angle CDB \) and \( \angle ADC \) are given in the ratio 4:5.

We know that:

1. \( \angle CDB \) + \( \angle ADC \) = 180° because they form a straight line (linear pair).

Given that the ratio of \( \angle CDB \) to \( \angle ADC \) is 4:5, let's assign:

- \( \angle CDB = 4x \)
- \( \angle ADC = 5x \)

Thus, the sum of the angles is:
\[
4x + 5x = 180°
\]
\[
9x = 180°
\]
\[
x = 20°
\]

Now, we can find the actual angles:

- \( \angle CDB = 4x = 4(20°) = 80° \)
- \( \angle ADC = 5x = 5(20°) = 100° \)

Thus, \( \angle CDB = 80° \) and \( \angle ADC = 100° \).

Would you like further clarification on this or related questions? Here are five related problems:

1. What are complementary and supplementary angles, and how do they relate to this problem?
2. How would the answer change if the ratio were 3:4 instead of 4:5?
3. Can you solve for angles if only their sum and one angle are given?
4. How do linear pairs of angles work in different geometric shapes?
5. What would happen if the lines weren't perpendicular—how would that affect the angles?

**Tip:** Always check the sum of angles on a straight line, which should equal 180°.

Given the diagram, if the ratio of angles ∠CDB : ∠ADC is 4:5, find the values of ∠ADC and ∠CDB.

Learn how to solve a geometry problem where the ratio of angles ∠CDB to ∠ADC is 4:5. This solution involves key geometric concepts such as linear pairs and the sum of angles on a straight line. Suitable for Grades 8-10.

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