In the given diagram, we are asked to find the measure of angle $\angle ACE$ given that $m \angle ACB = 66^\circ$.

Looking at the diagram:

• $\angle ACB$ is an angle formed by the intersection of lines $AB$ and $CD$ at point $C$.
• $\angle ACE$ involves the ray $CE$, which is perpendicular to $AB$, forming a right angle (denoted by the small square at $C$).

Since $\angle ACE$ is part of the straight line that includes the right angle $\angle ECF$, we can use the following property:

• $\angle ACE$ and $\angle ACB$ form a supplementary pair, since together they form the straight line $AB$.

Thus: $m \angle ACE + m \angle ACB = 90^\circ$ Substitute $m \angle ACB = 66^\circ$: $m \angle ACE = 90^\circ - 66^\circ = 24^\circ$

Therefore, $m \angle ACE = 24^\circ$.

Would you like further explanation or have any questions?

Here are some related questions you may find helpful:

1. What are supplementary angles?
2. How do you identify complementary angles in a geometry diagram?
3. What is the sum of the angles in a straight line?
4. How do perpendicular lines affect angle calculations?
5. How can you apply the concept of vertical angles to solve for unknown angles?

Tip: When dealing with angles around a point, always check for right angles and straight lines, as they simplify calculations using complementary and supplementary angle relationships.