To solve the problem in the image, let's break it down:

Given:

• Figure ABC is a quadrant.
• AEC and DEB are straight lines.
• ∠CDE = 63°.

We are asked to find ∠AEB.

Step-by-step solution:

1. Understanding the Geometry:

   • ABC is a quadrant, which means it is a quarter-circle. This suggests that the angle ∠ACB is 90° because it's part of a circle.
   • AEC and DEB are straight lines, so they will form certain angles in relation to the quadrant.
   • ∠CDE = 63°, which is given.

2. Identifying Key Relationships:

   • Since DEB is a straight line and passes through points D, E, and B, this means ∠AEB and ∠CDE are related via the straight line rule, which states that the sum of angles around a point on a straight line is 180°.

3. Using the Straight-Line Rule:

   • The sum of angles around point E must equal 180°.
   • Therefore, we have the equation: $∠AEB + ∠CDE = 180°$ Substituting the known value of ∠CDE (63°): $∠AEB + 63° = 180°$

4. Solving for ∠AEB:

   • Rearranging the equation: $∠AEB = 180° - 63°$ $∠AEB = 117°$

Thus, the value of ∠AEB is 117°.

Would you like further details or clarifications on any step?

Here are 5 related questions you might find useful:

1. How do you calculate angles in a circle?
2. What is the straight-line rule for angles?
3. How do different types of lines (straight vs curved) influence angle relationships?
4. How can you use the properties of quadrants in geometry problems?
5. What are other ways to verify the angle in this problem?

Tip: Always look for relationships between angles, such as complementary or supplementary, when dealing with straight lines and circles.