Choose an option (Data sufficiency based questions) : In an isosceles triangle ABC, what is the value of ∠C?-Statement 1: The measure of ∠A is 48∘-Statement 2: The measure of ∠B 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.
Q. Choose an option (Data sufficiency based questions) : In an isosceles triangle ABC, what is the value of ∠C?-Statement 1: The measure of ∠A is 48∘-Statement 2: The measure of ∠B 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.
Use Angle Properties: Use Statement 1: ∠A is 48∘. In an isosceles triangle, two angles are equal. If ∠A is 48∘, then ∠B or ∠C must also be 48∘. But we don't know which one is equal to ∠A.
Use Triangle Sum Property: Use Statement 2: ∠B is 96∘. Since the sum of angles in a triangle is 180∘, we can find the other two angles if we know one. But in an isosceles triangle, we need to know which two angles are equal to determine the third angle.
Combine Angle Statements: Combine Statements 1 and 2: If ∠A is 48∘ and ∠B is 96∘, then ∠C must also be 48∘ because it's an isosceles triangle and two angles must be equal. The sum of the angles would be 48∘+96∘+48∘=192∘, which is not possible because the sum of angles in a triangle must be 180∘. There's a mistake here.
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