GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag225

Prévia do material em texto

216 › Answers
321. (A) In a triangle, the sum of the lengths of any two sides must be greater than the 
length of the third side (triangle inequality). The lengths given in (A) satisfy this criterion. 
The lengths given in the other answer choices do not.
322. (D) Triangle ABC is isosceles, so ∠ = ∠m ABC m ACB. Given that ∠ ≅ABC ADE and 
∠ = °m ADE 63 , then ∠ = ∠ = °m ABC m ACB 63 . Thus, ∠ = ° − ° = °m A 180 2(63 ) 54 .
323. (C) Let 2x = the measure of the smallest angle. Then the measures of the other two 
angles are 3x and 5x. Thus,
+ + = °
= °
= °
= °
x x x
x
x
x
2 3 5 180
10 180
18
2 36 
324. (E) Let x = the length of the third side of the triangle. Of the lengths 3, 7, and x, 
the longest side is either 7 or x. If the longest side is 7, by the triangle inequality, + >x3 7, 
which implies x > 4. If the longest side is x, by the triangle inequality, + > x3 7 , which 
implies 10 > x. Therefore, the third side must have a length between 4 and 10. The possible 
whole number lengths are 5, 6, 7, 8, and 9, so five triangles are possible.
325. (D) Let x = ∠Bthe measure of . Then + ° = ∠x A25 the measure of . And 2x − 9° = the 
measure of ∠C. Write an equation and solve for x.
+ + ° + − ° = °
+ + ° + − ° = °
= °
= ° = ∠
+ ° = ° = ∠
− ° = ° = ∠
x x x
x x x
x
x B
x A
x C
( 25 ) (2 9 ) 180
25 2 9 180
4 164
41 the measure of
25 66 the measure of
2 9 73 the measure of , the largest angle 
326. (A) Consecutive angles of a parallelogram are supplementary, so write an equation 
and solve for x.
 
− ° + + ° = °
− °+ + ° = °
= °
= °
x x
x x
x
x
( 30 ) (2 60 ) 180
30 2 60 180
3 150
50 
 − ° = °x 30 20 , the measure of the smaller angle
327. (E) For any triangle, if P, Q, and R are the midpoints of the sides, the perimeter 
of triangle PQR is one-half the perimeter of the original triangle because the segment 
between the midpoints of any two sides of a triangle is half as long as the third side. Thus, 
07_McCune_Answer.indd 216 2/21/22 4:37 PM