Is one of the angles of the quadrilateral ABC...
Is one of the angles of the quadrilateral ABCD equal to 90 degrees?
(1) ABCD is a parallelogram
(2) One of the interior angles of ABCD is equal to 60 degrees
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to
• d)
EACH statement ALONE is sufficient to answer the question
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to
problem are needed.

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 PATEL KRISTAL MAHENDRABHAI Sep 15, 2019
Related Is one of the angles of the quadrilateral ABCD equal to 90 degrees?(1) ABCD is a parallelogram(2) One of the interior angles of ABCD is equal to 60 degreesa)Statement (1) ALONE is sufficient, but statement (2) alone isnot sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone isnot sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient toanswer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?
Step 1 & 2: Understand Question and Draw Inference
Given
To Find
• Is one of the angles of quadrilateral ABCD = 90o
• Let the angles be a, b, c and d. Hence a + b + c+ d= 360o
Step 3 : Analyze Statement 1 independent
(1) Statement 1 states that "ABCD is a parallelogram"
• For a parallelogram opposite angles are equal,
• Thus, a = c and b = d. Also, a + d = 180 and b + c = 180
• However, it does not tell us about the value of the angles of the quadrilateral.
• Hence Statement 1 is Insufficient to answer the question.
Step 4 : Analyze Statement 2 independent
(2) Statement 2 states that "One of the interior angles of ABCD is equal to 60 degrees"
• a = 60o
• b + c + d = 300o
• However, this does not tell us about the value of the other 3 angles.
• Hence Statement 2 is also insufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
• As a = 60o , c = 60o
• b+ d = 240o
• 2b = 240o
• b=d= 120o
• ​Hence, by combining both the statements we can get the answer.
• Therefore, the correct answer is Option C .

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