GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag224

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Answers ‹ 215
316. (E) Make a sketch, filling in the question information.
36 °
A
C
B
 Angles C and B are base angles of an isosceles triangle, so they are congruent: 
m B m C 36∠ = ∠ = °. The sum of the measures of a triangle’s angles is 180°. Thus, 
m A 180 2(36 ) 180 72 108∠ = ° − ° = ° − ° = °.
317. (B)
m AQC m AQB m BQC∠ = ∠ + ∠ 
 ∠ + ∠ + ∠ + ∠ = °m AQP m AQB m BQC m CQR 180 
 Given ∠ ≅ ∠AQP AQB and ∠ ≅ ∠BQC CQR , then ∠ + ∠ = °m AQB m BQC2( ) 2( ) 180 . 
Thus, ∠ + ∠ = ° = ∠m AQB m BQC m AQC90 .
318. (C) ∠3 is congruent to the vertical angle between ∠1 and ∠2. Therefore, 
∠ + ∠ + ∠ = °m m m1 2 3 180 . Thus, °+ °+ ∠ = °m65 85 3 180 , so ∠ = °m 3 30 .
319. (C) List the triangles, proceeding systematically. You have triangles ABC, ABD, ABE, 
ACD, ADE, BCD, BCE, and CDE for a total of 8 triangles.
320. (C) Make a sketch, filling in the question information.
35°
SR
Q
P
NM
 ≅RP PS, ∠ ≅ ∠RPQ SPQ , and ≅PQ PQ . Therefore, PQR PQS because two sides 
and the included angle of PQR are congruent to the corresponding parts of PQS . Thus, 
∠ = ∠ = °m PQR m PQS 35 (corresponding parts of congruent triangles are congruent). 
Given that PQ is perpendicular to MN , ∠ = ° − ° = °m RQM 90 35 55 .
07_McCune_Answer.indd 215 2/21/22 4:37 PM