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What is the Sum of the Angles?

Discussion in 'CAT/MAT/GMAT Preparation' started by Royaluni, Sep 11, 2015.

  1. Royaluni

    Royaluni Administrator

    GMAT Practice Question--In the figure shown, what is the value of v+x+y+z+w?

    geometry question gmat practice.jpg

    A. 45

    B. 90

    C. 180

    D. 270

    E. 360

    Answer – it is a geometry question with algebra, we first need to identify the geometrical shapes and then use geometrical concepts and formulas to create an equation. Then we will solve that equation with algebraic methodology to find out the desired value.

    Now take a lot at this picture;
    pentagon angles.jpg

    Point marked as a,b,c,d,e forms a pentagon. Total sum of interior angles of a Polygon is;

    180(n-2) where n is the number of sides

    In our case, it is pentagon, so total 5 sides;

    180(5-2)=540

    Now if you see diagram carefully, you will find that each point in pentagon is the third angle of triangle. So we have following triangles;

    avz , ewy,dzx,cyv,bxw

    Now sum of the angles of each triangle will be 180

    A+v+z = 180

    E+w+y=180

    D+z+x=180

    C+y+v=180

    B+x+w=180

    Now if we add all the above 5 equations, we get;

    A+b+c+d+e+2v+2w+2z+2y+2x=900

    We have already determined that the sum of all the angles of a pentagon is 540, so we will replace that value in the above equation for our pentagon-abcde

    5402v+2w+2z+2y+2x=900

    2v+2w+2z+2y+2x=900-540

    2v+2w+2z+2y+2x=360

    Simplify

    2(v+w+z+y+x)=360

    v+w+z+y+x=360/2=180

    answer choice is C

    If 5 were to be added to each score, which of these three statistics would change.
     

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