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# If RS = ST = TR in the figure above, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
Posts: 55271
If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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01 Sep 2017, 00:46
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Difficulty:

15% (low)

Question Stats:

97% (00:22) correct 3% (00:02) wrong based on 59 sessions

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If RS = ST = TR in the figure above, what is the value of x?

(A) 60
(B) 90
(C) 120
(D) 135
(E) 180

Attachment:

2017-09-01_1134_002.png [ 6.34 KiB | Viewed 1289 times ]

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If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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Updated on: 01 Sep 2017, 03:51
2

The information given indicates that RST is an equilateral triangle making $$x^{\circ} = 180^{\circ} - {\angle}SRT = 180^{\circ}-60^{\circ} = 120^{\circ}$$

Originally posted by sanahazari on 01 Sep 2017, 03:25.
Last edited by sanahazari on 01 Sep 2017, 03:51, edited 1 time in total.
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Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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01 Sep 2017, 03:41
The triangle is equilateral. Hence, all angles are 60 degrees. Since angle x is created by merely extending RT, we can conclude that the measure of x is 180-60 = 120 degrees
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Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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01 Sep 2017, 10:10
given a equilateral triangle .... all sides at 60.
x = 180 - 60 = 120
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Posts: 2183
Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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02 Sep 2017, 05:45
Bunuel wrote:

If RS = ST = TR in the figure above, what is the value of x?

(A) 60
(B) 90
(C) 120
(D) 135
(E) 180

Attachment:
2017-09-01_1134_002.png

Equilateral triangle means all angles = 60

so x =180 -60 =120

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Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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02 Sep 2017, 07:21
Bunuel wrote:

If RS = ST = TR in the figure above, what is the value of x?

(A) 60
(B) 90
(C) 120
(D) 135
(E) 180

Attachment:
2017-09-01_1134_002.png

RS=ST=TR implies the triangle is an equilateral triangle with each angle 60.

we know that x+60 =180 as they are angles on the line. So x=120.

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Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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07 Sep 2017, 07:11
Bunuel wrote:

If RS = ST = TR in the figure above, what is the value of x?

(A) 60
(B) 90
(C) 120
(D) 135
(E) 180

Since we have an equilateral triangle, each interior angle is 60 degrees, and thus x = 180 - 60 = 120.

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Re: If RS = ST = TR in the figure above, what is the value of x?  [#permalink]

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07 Sep 2017, 22:12
As RS= ST=TR , it is equilateral triangle with each angle measures 60.

So, x = angle RST + angle STR (An exterior angle of a triangle is equal to the sum of the opposite interior angles)
= 60 +60
= 120

Re: If RS = ST = TR in the figure above, what is the value of x?   [#permalink] 07 Sep 2017, 22:12
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