1994 AMC 8 Problem 7 — Solution | LIVE by Po-Shen Loh

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1994 AMC 8 Problem 7

Attempt Problem 7 of the 1994 AMC 8 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 1994 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

If $\angle A = 60°,$ $\angle E = 40°,$ and $\angle C = 30°,$ then $\angle BDC =$

$40°$

$50°$

$60°$

$70°$

$80°$

Answer: B

Concepts:angle chasing angle sum

Difficulty rating: 920

Solution:

In triangle $ABE,$ $\angle ABE = 180°$ $- (60° + 40°)$ $= 80°.$

Since $A, B, C$ are collinear and $D$ lies on segment $EB,$ the angle $\angle DBC = 180° - 80° = 100°.$

In triangle $BDC,$ $\angle BDC = 180°$ $- (100° + 30°)$ $= 50°.$

Thus, the correct answer is B .

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