Question

In isosceles triangle ABC, what is the value of \(\angle LC\)? (1) The measure of \(\angle LB\) is 47°
(2) The measure of \(\angle LA\) is 96°
 

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• D. EACH statement ALONE is sufficient.
• E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hint:

In an isosceles triangle, two angles are always equal. Use this property to find missing angles.

Answer 1

The Correct Option is C

Step 1: Analyze Statement (1). 
In an isosceles triangle, two angles are equal. If \(\angle LB = 47\degree\), then \(\angle LC = 47\degree\), since these two angles must be equal. 
Step 2: Analyze Statement (2). 
If \(\angle LA = 96\degree\), and since this is an isosceles triangle, \(\angle LB = \angle LC\). Thus, knowing \(\angle LA = 96\degree\) doesn't directly provide the value for \(\angle LC\). Step 3: Combine Statements. 
Combining both statements, we know the two equal angles (\(\angle LB\) and \(\angle LC\)) sum up to \(180\degree - 96\degree = 84\degree\). Hence, each of these angles is: \[ \frac{84}{2} = 42\degree \] Thus, the value of \(\angle LC = 42\degree\). 
Final Answer: \[ \boxed{C} \]