GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag201

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206. 170 The sum of the measures of the interior angles of an n-sided convex polygon is 
− °n( 2)180 . For a pentagon, this sum is − °(5 2)180 = °(3)180 = °540 . From the informa-
tion in the figure, + °x6 2 is the greatest of the measures of the angles. Write and solve the 
following equation, and then compute + °x6 2 :
 − ° + + + ° + − ° + = °x x x x x(2 14 ) (2 ) (6 2 ) (4 8 ) 6 540 
 − ° = °x20 20 540 
 x20 = °560 
 x = °28 
 + ° = ⋅ °+ °x6 2 6 28 2 = °170 
207. 5 The area of triangle RYQ = = RQ YQ45
1
2
( )( ), which implies that =RQ YQ( )( ) 90. 
Also, the area of triangle RPY = 90 = RQ PY
1
2
( )( ), which implies that =RQ PY( )( ) 180. 
Thus, =RQ YQ RQ PY( )( )
1
2
( )( ); =YQ PY( )
1
2
( ) = =
1
2
(10) 5. From the figure, XQ = 
+XY YQ = 10. Substituting =YQ 5 gives +XY 5 = 10; XY = 5.
208. 8 The volume, V, of the cylindrical tank is πr h2 , where r is the radius of its circular 
base and h is the height of the cylinder. From the question information, write and solve the 
following equation for r, and then compute d = 2r :
 3
4
 V = π π=r h r
3
4
3
4
(8 ft)2 2 = π96 cubic feet
 Omitting units and solving for r,
 π π=r
3
4
(8) 962
 =r 162
 r = 4
 d = = ⋅ =r2 2 4 8 feet
209. 21 From the figure, XY = + +z( 12) 3. Because XY and UV are intersecting chords in 
a circle, =XW WY UW WV( )( ) ( )( ). Solve the following equation, and then compute XY = 
+ +z( 12) 3:
 + = +z z z( 12)(3) ( 3)( )
 + = +z z z3 36 32 
 = z36 2 
 z = 6 (because you can assume that, as a measurement of length, z is positive)
 = + +XY z( 12) 3 = + + =(6 12) 3 21 
06_McCune_Answer.indd 192 2/21/22 4:48 PM