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16 Sep 2014, 00:58
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Is triangle \(ABC\) a right triangle?
(1) \(\angle ABC = \angle BCA\)
(2) \(\angle ABC = \angle CAB + 30\) degrees
(1) \(\angle ABC = \angle BCA\)
(2) \(\angle ABC = \angle CAB + 30\) degrees
16 Sep 2014, 00:58
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Official Solution:
Statement (1) by itself is insufficient. The triangle is isosceles but this imposes no restrictions on angle \(CAB\).
Statement (2) by itself is insufficient. Assigning different values to angle \(CAB\), we will get different triangles. If \(CAB = 60\) or \(30\), the triangle is a right triangle.
Statements (1) and (2) combined are sufficient. S1 and S2 provide a system of three linear equations (the third equation is derived from the condition that the sum of the angles equals 180 degrees) with three unknown variables. From this system, we can find the value of each angle.
Answer: C
Statement (1) by itself is insufficient. The triangle is isosceles but this imposes no restrictions on angle \(CAB\).
Statement (2) by itself is insufficient. Assigning different values to angle \(CAB\), we will get different triangles. If \(CAB = 60\) or \(30\), the triangle is a right triangle.
Statements (1) and (2) combined are sufficient. S1 and S2 provide a system of three linear equations (the third equation is derived from the condition that the sum of the angles equals 180 degrees) with three unknown variables. From this system, we can find the value of each angle.
Answer: C
13 Jul 2016, 11:15
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Hello,
Can you please share how the property that all interior angles sum to 180 helps us get answer C. Thanks in advance for your help?
Can you please share how the property that all interior angles sum to 180 helps us get answer C. Thanks in advance for your help?
