Angles
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Source: Beat The GMAT — Data Sufficiency |
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Question: In the figure shown, what is the value of x?
Statement 1: The length of line segment QR is equal to the length of line segment RS.
There are multiple ways to show that this statement is insufficient. For one thing, U could be anywhere on side PT. So even if we somehow were to know the exact measures of all the angles of triangle QRS, which we don't, x could still have a variety of values.
Insufficient.
Statement 2: The length of line segment ST is equal to the length of line segment TU.
Since Q could be anywhere on side PR, angle x could have a variety of values even if we were to know the measures of the angles of triangle STU, which we don't.
Insufficient.
Statements Combined:
This is one of those cool GMAT quant questions which you can answer without having a way to determine many of the values involved.
Since the angle at P is a right angle and the angles of a triangle add up to 180 degrees, we know that the angles at R and T add up to 90 degrees.
Since the total degrees of the angles of triangles QRS and STU must be 2 x 180 = 360 degrees, we can subtract the measures of the angles at R and T to find that the totals of the measures of the base angles of the two triangles are 360 - 90 = 270.
Since QR = RS and ST = TU the two triangles are isosceles triangles, meaning that their base angles are equal. Therefore to get the total of the measures of angles QSR and UST, we can divide 270 by 2 to get 135. To get x, subract 135 from 180 to get 45.
Sufficient.
The correct answer is C.
Statement 1: The length of line segment QR is equal to the length of line segment RS.
There are multiple ways to show that this statement is insufficient. For one thing, U could be anywhere on side PT. So even if we somehow were to know the exact measures of all the angles of triangle QRS, which we don't, x could still have a variety of values.
Insufficient.
Statement 2: The length of line segment ST is equal to the length of line segment TU.
Since Q could be anywhere on side PR, angle x could have a variety of values even if we were to know the measures of the angles of triangle STU, which we don't.
Insufficient.
Statements Combined:
This is one of those cool GMAT quant questions which you can answer without having a way to determine many of the values involved.
Since the angle at P is a right angle and the angles of a triangle add up to 180 degrees, we know that the angles at R and T add up to 90 degrees.
Since the total degrees of the angles of triangles QRS and STU must be 2 x 180 = 360 degrees, we can subtract the measures of the angles at R and T to find that the totals of the measures of the base angles of the two triangles are 360 - 90 = 270.
Since QR = RS and ST = TU the two triangles are isosceles triangles, meaning that their base angles are equal. Therefore to get the total of the measures of angles QSR and UST, we can divide 270 by 2 to get 135. To get x, subract 135 from 180 to get 45.
Sufficient.
The correct answer is C.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
