1968 AHSME Problems/Problem 6
Problem
Let side of convex quadrilateral be extended through , and let side be extended through , to meet in point Let be the degree-sum of angles and , and let represent the degree-sum of angles and If , then:
Solution
Because is a convex quadrilateral, the sum of its interior angles is . Thus, . Furthermore, because and are supplementary to and , respectively, the four angles sum to , so . Plussing this expression for into the first equation, we see that , so , which is answer choice .
See also
1968 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.