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Choose an option (Data sufficiency based questions) : In an isosceles triangle ABCABC, what is the value of C\angle C?\newline-Statement 11: The measure of A\angle A is 4848^\circ\newline-Statement 22: The measure of B\angle B is 9696^\circ\newlinea. Statement (11) ALONE is sufficient, but statement (22) alone is not sufficient.\newlineb. Statement (22) ALONE is sufficient, but statement (11) alone is not sufficient.\newlinec. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.\newlined. EACH statement ALONE is sufficient.\newlinee. Statements (11) and (22) TOGETHER are not sufficient.

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Q. Choose an option (Data sufficiency based questions) : In an isosceles triangle ABCABC, what is the value of C\angle C?\newline-Statement 11: The measure of A\angle A is 4848^\circ\newline-Statement 22: The measure of B\angle B is 9696^\circ\newlinea. Statement (11) ALONE is sufficient, but statement (22) alone is not sufficient.\newlineb. Statement (22) ALONE is sufficient, but statement (11) alone is not sufficient.\newlinec. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.\newlined. EACH statement ALONE is sufficient.\newlinee. Statements (11) and (22) TOGETHER are not sufficient.
  1. Use Angle Properties: Use Statement 11: A\angle A is 4848^\circ. In an isosceles triangle, two angles are equal. If A\angle A is 4848^\circ, then B\angle B or C\angle C must also be 4848^\circ. But we don't know which one is equal to A\angle A.
  2. Use Triangle Sum Property: Use Statement 22: B\angle B is 9696^\circ. Since the sum of angles in a triangle is 180180^\circ, 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.
  3. Combine Angle Statements: Combine Statements 11 and 22: If A\angle A is 4848^\circ and B\angle B is 9696^\circ, then C\angle C must also be 4848^\circ because it's an isosceles triangle and two angles must be equal. The sum of the angles would be 48+96+48=19248^\circ + 96^\circ + 48^\circ = 192^\circ, which is not possible because the sum of angles in a triangle must be 180180^\circ. There's a mistake here.

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