1970 AMC 12 Problem 30
Attempt Problem 30 of the 1970 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1970 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
In the accompanying figure, segments and are parallel, the measure of angle is twice that of angle and the measures of segments and are and respectively. Then the measure of is equal to:
Answer: E
Small hint:
Bisect angle and let the bisector meet at
Big hint:
Angle chasing makes isosceles, while is a parallelogram
Solution:
Let the bisector of meet at Because each half has measure Since the alternate interior angle also equals Thus triangle is isosceles and Also and so is a parallelogram. Hence Therefore
Therefore, the correct answer is E.
Problem 30 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
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- 1961 AMC 12
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- 1963 AMC 12
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- 1972 AMC 12
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