## 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?

- s = 40
- r = 70

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Geometry |

Sub-Topic | Triangles |

Difficulty | Easy – Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__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__

__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__

__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)__

__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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