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RST is isosceles

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RST is isosceles [#permalink] New post 17 Mar 2018, 03:17
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Question Stats:

48% (00:36) correct 51% (00:31) wrong based on 35 sessions
\(\Delta RS\)T is isosceles and \(\angle RST = 40\)degrees


Quantity A
Quantity B
The sum of the measures of the two angles \(\angle RST\) that have equal measure
\(120\) degrees



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: RST is isosceles [#permalink] New post 17 Mar 2018, 23:15
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Explanation

Given RST is an isosceles triangle and one measure of angle \(= 40\) degrees
It could be that another angle also measures 40 degrees and the third angle of the triangle measures \(100\) degrees as sum of angles in a triangle add to \(180\)degrees

Or, It could be the case that one angle is \(40\) and the remaining \(140\) degree is equally divided among the two angles of \(70\) degree each
Hence sum of two angles could be \(40 + 40 =80\) or \(70 + 70 = 140\)
Therefore sum of angles of RST could either be greater than or smaller than 120
Hence D
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Re: RST is isosceles [#permalink] New post 02 Apr 2018, 12:36
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Answer: D
RST is a triangle with two same edges and sides. So it’s degree will be 2e + x = 180
*there is a tale in this question, the two equal angels might be both 40 and the other angel 180 - 40* 2 = 100 or might be 70 and the third angel be 40. So there are two conditions, not one.

In the first condition, As one angle equals 40, the other similar one is also 40 and the third one is x = (180 - 2e) = (180 - 2*40) = 100
The sum of the measures of the two equal angels (2e) is 2*40 = 80 and thus B is bigger than A.

In the second condition, As the third angel equals 40, the two similar ones are e = (180 - x )/2 = (180 - 40) / 2 = 70
The sum of the measures of the two equal angels (2e) is 2*70 = 140 and thus A is bigger than B.

The answer is D as there are two different conditions.
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Re: RST is isosceles [#permalink] New post 04 Apr 2018, 06:44
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Quantity A: We are not given whether the angle RST is one of the two angles that are equal. So, there can be two cases:
Case1: If Angle RST is one of the angles, then the sum of angles of equal measure would be 80 degrees.
Case2: If Angle RST is not one of the angles, then sum of the angles of equal measure would be (180-40) degrees

QuantityB: 120 degrees

Hence option D
Re: RST is isosceles   [#permalink] 04 Apr 2018, 06:44
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