1990 AHSME Problems/Problem 20
Problem
In the figure is a quadrilateral with right angles at and . Points and are on , and and are perpendicual to . If and , then
Solution
Label the angles as shown in the diagram. Since forms a linear pair with , is a right angle.
Let and .
Since , and , then . By the same logic, .
As a result, . By the same logic, .
Then, , and .
Then, , and .
By the transitive property, . , and plugging in, we get .
Finally, plugging in to , we get
See also
1990 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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