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In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. – OG 2020 Question #306 with Solution

OG 2020: Question No. 306

In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y?

  1. s = 40
  2. r = 70
SourceOG 2020
TypeData Sufficiency
TopicGeometry
Sub-TopicTriangles
DifficultyEasy – Medium

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

  • A diagram representing a triangle RST
  • Angle SRT = r°, angle RTS = t° and angle TSR = s°
  • PRTQ is a line segment
  • Angle PRS = x° and angle QTS = y°

We need to determine

  • The value of x + y

As PRTQ is a line segment, we can say

  • x + r = t + y = 180°
  • Therefore, x + r + t + y = 180 + 180 = 360
    • Or, x + y = 360 – (r + t)

Hence, to find the value of x + y, we need to know either the individual values of r and t, or their sum.

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, s = 40.

Also, because RST is a triangle, we can say r + s + t = 180

  • Or, r + 40 + t = 180

Or, r + t = 180 – 40 = 140

As we can determine the value of r + t, we will be able to determine x + y also.

Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, r = 70

  • From this statement, we do not get any information about the value of t.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer choice is option A.

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