Difference between revisions of "1986 AHSME Problems/Problem 3"
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==Problem== | ==Problem== | ||
− | <math>\triangle ABC</math> | + | <math>\triangle ABC</math> has a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>) is the bisector of <math>\angle ABC</math>, then <math>\angle BDC =</math> |
<math>\textbf{(A)}\ 40^\circ \qquad | <math>\textbf{(A)}\ 40^\circ \qquad | ||
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==Solution== | ==Solution== | ||
− | + | Since <math>\angle C = 90^{\circ}</math> and <math>\angle A = 20^{\circ}</math>, we have <math>\angle ABC = 70^{\circ}</math>. Thus <math>\angle DBC = 35^{\circ}</math>. It follows that <math>\angle BDC = 90^{\circ} - 35^{\circ} = 55^{\circ}</math>, which is <math>\boxed{D}</math>. | |
== See also == | == See also == |
Latest revision as of 17:03, 1 April 2018
Problem
has a right angle at and . If ( in ) is the bisector of , then
Solution
Since and , we have . Thus . It follows that , which is .
See also
1986 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 | ||
All AHSME Problems and Solutions |
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