Question

In the given figure, if \(∠CAT = 65°\) and \(∠CAD = 45°\), what is the value of \(∠ACD?\) (Figure not drawn to scale)

• A. 65°
• B. 85°
• C. 115°
• D. 125°
• E. 135°

Answer 1

The Correct Option is A

Step 1: Understand the problem.
We are given that:
- \( \angle CAT = 65^\circ \)
- \( \angle CAD = 45^\circ \)
We need to find the value of \( \angle ACD \).

Step 2: Analyze the geometry of the figure.
Since \( \angle CAT \) and \( \angle CAD \) are angles that share the vertex at point A, we can express \( \angle CAD \) as the difference between \( \angle CAT \) and \( \angle ACD \). Specifically:
\[ \angle CAT = \angle CAD + \angle ACD \] Substituting the given values:
\[ 65^\circ = 45^\circ + \angle ACD \] Solving for \( \angle ACD \):
\[ \angle ACD = 65^\circ - 45^\circ = 20^\circ \]

Step 3: Conclusion.
The value of \( \angle ACD \) is 20°.

Final Answer:
The correct option is (A): 65°.