AMC10 2007 B

AMC10 2007 B · Q15

AMC10 2007 B · Q15. It mainly tests Polygons.

The angles of quadrilateral ABCD satisfy $\angle A = 2\angle B = 3\angle C = 4\angle D$. What is the degree measure of $\angle A$, rounded to the nearest whole number?

四边形ABCD的内角满足$\angle A = 2\angle B = 3\angle C = 4\angle D$。$\angle A$的度数，四舍五入到最接近的整数是多少？

(A) 125 125

(B) 144 144

(D) 173 173

(E) 180 180

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Let $x$ be the degree measure of $\angle A$. Then the degree measures of angles $B$, $C$, and $D$ are $x/2$, $x/3$, and $x/4$, respectively. The degree measures of the four angles have a sum of $360$, so \[ 360 = x + \frac{x}{2} + \frac{x}{3} + \frac{x}{4} = \frac{25x}{12}. \] Thus $x = (12 \cdot 360)/25 = 172.8 \approx 173$.

答案（D）：设 $x$ 为 $\angle A$ 的度数。则角 $B$、$C$、$D$ 的度数分别为 $x/2$、$x/3$、$x/4$。四个角的度数和为 $360$，因此 \[ 360 = x + \frac{x}{2} + \frac{x}{3} + \frac{x}{4} = \frac{25x}{12}. \] 所以 $x = (12 \cdot 360)/25 = 172.8 \approx 173$。

Topics

GE.008 Polygons