1980 AMC 12 Problem 4

Attempt Problem 4 of the 1980 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 1980 AMC 12 solutions, or check the answer key.

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

In the adjoining figure,

CDE

is an equilateral triangle and

ABCD

and

DEFG

are squares. The measure of

\angle GDA

90^\circ

105^\circ

120^\circ

135^\circ

150^\circ

Identify the three known angles at

D

Use the full

360^\circ

angle around point

D

D,

the two square angles are

90^\circ

each and the equilateral-triangle angle is

60^\circ.

Hence

\begin{aligned} \angle GDA &=360^\circ-90^\circ\\ &\quad-60^\circ-90^\circ\\ &=120^\circ. \end{aligned}

Therefore, the correct answer is C.

Problem 4 in other years