In this problem, we're given that AB is parallel to DE, ∠ABC = 35°, and ∠CDE = 250°. We are asked to find the angle ∠ACD and to state our reasoning clearly.

Step 1: Understand the Given Information

• AB is parallel to DE: This tells us that the lines AB and DE will never meet, implying certain angle relationships due to parallelism.
• ∠ABC = 35°: This is the angle formed by the line segments AB and BC.
• ∠CDE = 250°: This is an external angle at point D.

Step 2: Analyze the Parallel Lines

Since AB is parallel to DE, and the transversal AC cuts across both lines, we can use the properties of parallel lines to determine relationships between angles.

• Interior Angles on the Same Side of the Transversal: If AB and DE are parallel, then the angles on the same side of the transversal AC should add up to 180°. Specifically, ∠ABC and the angle adjacent to ∠CDE along the line DE (which would be 360° - 250° = 110°) are corresponding angles.

Step 3: Calculate ∠ACD

• Since the sum of corresponding angles on the same side of a transversal is 180°: $\text{Let } x = \angle ACD$ By the exterior angle theorem: $x = 180° - \angle ABC$ Substituting the given value of ∠ABC = 35°: $x = 180° - 35° = 145°$ Thus, ∠ACD = 145°.

Final Answer

• ∠ACD = 145°

This is the required angle, based on the properties of parallel lines and the exterior angle theorem.

Do you want further details or have any questions about this explanation?

Further Related Questions:

1. What is the significance of parallel lines in determining angle relationships?
2. How can the exterior angle theorem be applied in other geometric problems?
3. What are the conditions for two lines to be considered parallel?
4. How does the concept of transversal lines help in solving geometry problems?
5. How can you find unknown angles when given parallel lines and a transversal?

Tip:

Always check for parallel lines and transversal angles in geometric diagrams; they often provide shortcuts to finding unknown angles.