Math Challenge #24: Quantity A : The value of x + y + z | QuantityB: 270
Quantity A
The value of x + y + z
Quantity B
270
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Explanation with Answer:
Correct Choice:(B)Angle in the pentagon is labeled with the same variable, so this is a regular pentagon. Using the formula (n - 2)(180) [ where n is the number of sides ]
the sum of all the interior angles of the pentagon is (3)(180) = 540
degrees. Divide by 5 to get x = 108.
Now, the quadrilateral. All four-sided figures have interior angles that sum to 360. If you didn’t have that memorized, you could also use (n - 2)(180) to determine this. Divide 360 by 4 to get y = 90.
Now, the triangle. It is equilateral, so z = 60. (The sum of angle measures in a triangle is always 180; if the angles are equal, they will each equal 60.)
Thus, x + y + z = 108 + 90 + 60 = 258.
Quantity B is greater.
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