Multiple Figures

Geometry: Multiple Figures

Read the following SAT test question and then select the correct answer. 

Use the same steps for every math problem.  First, read the question carefully and identify the bottom line.  Next, assess your options and choose the most efficient method to attack the problem.  Finally, loop back to verify that your answer addresses the bottom line.

In the figure above, if PQRS is a quadrilateral and TUV is a triangle, what is the sum of the degree measures of the marked angles?

Bottom Line:  Sum of degrees of the marked angles = ? (Write Sd = ?)

Assess your Options:  You could try to find the individual angles, but you don’t have enough information to do this.  Instead, use the rules you have memorized about each shape.

Attack the Problem:  You know that TUV is a triangle.  All the angles of a triangle add up to 180 degrees.  You know that PQRS is a quadrilateral.  All the angles of a quadrilateral add up to 360 degrees.  In the image, you can see that all of these angles in each of these two shapes are marked, and you know that you are looking for a sum, so add them together.  180 + 360 = 540.

Loop back: Your answer is in degrees and you have found the total of all the marked angles.  Look down at your answer choices.

(A) 420

(B) 490

(C) 540

(D) 560

(E) 580

The correct answer is (C).

On sat.collegeboard.org, 77% of the responses were correct.

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