GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag246

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Answers ‹ 237
 (A) AD AB> , False [see explanation for (B)]. (B) AC AD> , True. m ADB m C∠ > ∠ (the 
measure of an exterior angle of a triangle is greater than the measure of either nonadjacent 
interior angle). m B m C∠ = ∠ (base angles of an isosceles triangle are congruent). Hence, 
m ADB m B∠ > ∠ , which implies AB AD> (AB is opposite the greater angle in ABD). 
AB AC≅ , so AB AC AD= > . (C) m B m C∠ = ∠ , True (base angles of an isosceles triangle 
are congruent). (D) m B m ADB∠ > ∠ , False [see explanation for (B)]. (E) m C m ADC∠ > ∠ , 
False. m ADC m B∠ > ∠ (the measure of an exterior angle of a triangle is greater than the 
measure of either nonadjacent interior angle). m B m C∠ = ∠ (base angles of an isosceles 
triangle are congruent). Hence, m ADC m C∠ > ∠ .
451. (A), (C), (E) Select (A) because AP PC≅ , BP PD≅ , and APB CPD∠ ≅ ∠ (vertical 
angles are congruent) implies APB CPD by SAS. Select (C) because by (A) AB CD≅ 
(corresponding parts of congruent triangles are congruent), so AB CD= . Select (E) because 
A C∠ ≅ ∠ (corresponding parts of congruent triangles are congruent). Thus, AB CD (alter-
nate interior angles of parallel lines are congruent).
452. (B), (C) The sum of the measures of the angles of a triangle is 180°. The angle mea-
sures given in (B) and (C) satisfy this criterion. The angle measures given in the other answer 
choices do not.
453. (A), (B), (D) The sum of the measures of the five interior angles of a pentagon is 
(5 2)180− ° = 3 180⋅ ° = 540°. Thus, the sum of the measures of the three remaining angles 
is 540 100 120 320° − ° − ° = °. Select (A), (B), and (D).
454. (B) The measure, m, of an interior angle of an n-sided regular polygon is 
m n
n
( 2)180= − ° . Solving m n
n
( 2)180= − ° for n yields n
m
360
180
= °
° −
. Thus, because n is 
a whole number, 360° must be divisible by m(180 )° − . Eliminate (A) because 360° is not 
divisible by 105 ( 180 75 )° = ° − ° . Select (B) because 360° divided by 90 ( 180 90 )° = ° − ° is 4. 
Eliminate (C) because 360° is not divisible by 80 ( 180 100 )° = ° − ° . Eliminate (D) because 
360° is not divisible by 52 ( 180 128 )° = ° − ° . Eliminate (E) because 240 180° > °.
455. (A), (B), (D), (E), (F) The measures of the exterior angles are °30 , °45 , °60 , 
°90 , and °120 . The measure, m, of an exterior angle of an n-sided regular polygon is 
m
n
360= ° . Select (A) because 360
3
120° = °. Select (B) because 360
4
90° = °. Eliminate (C) 
because 360
5
72° = °. Select (D) because 360
6
60° = °. Select (E) because 360
8
45° = °. Select 
(F) because 360
12
30° = °.
456. (A), (D), (F) Make a sketch. (A) True (a diagonal divides a parallelogram into two 
congruent triangles). (D) True (alternate interior angles of parallel lines are congruent). 
(F) True (the diagonals of a parallelogram bisect each other).
D C
BA
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