AMC8 1997

AMC8 1997 · Q12

AMC8 1997 · Q12. It mainly tests Angle chasing, Triangles (properties).

$\angle 1 + \angle 2 = 180^\circ$ $\angle 3 = \angle 4$ Find $\angle 4$ (figure with angles 40° and 70° shown).

$\angle1+\angle2=180^\circ$ $\angle3=\angle4$ 求 $\angle4$（图中标有 $40^\circ$ 和 $70^\circ$）。

(A) 20° 20°

(B) 25° 25°

(D) 35° 35°

(E) 40° 40°

Answer

Correct choice: (D)

正确答案：（D）

Solution

Triangle sum: $40^\circ + 70^\circ + \angle 1 = 180^\circ$, so $\angle 1 = 70^\circ$, $\angle 2 = 110^\circ$. Then $110^\circ + 2\angle 4 = 180^\circ$, $\angle 4 = 35^\circ$.

三角形内角和：$40^\circ+70^\circ+\angle1=180^\circ$，故 $\angle1=70^\circ$，$\angle2=110^\circ$。然后 $110^\circ+2\angle4=180^\circ$，$\angle4=35^\circ$。

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