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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