AMC12 2002 A

AMC12 2002 A · Q4

AMC12 2002 A · Q4. It mainly tests Linear equations, Angle chasing.

Find the degree measure of an angle whose complement is 25% of its supplement.

求一个角的度数，使得它的余角是它的补角的 25%。

(A) 48 48

(B) 60 60

(D) 120 120

(E) 150 150

Answer

Correct choice: (B)

正确答案：（B）

Solution

We can create an equation for the question, $4(90-x)=(180-x)$ $360-4x=180-x$ $3x=180$ After simplifying, we get $x=60 \Rightarrow \mathrm {(B)}$ Given that the complementary angle is $\frac{1}{4}$ of the supplementary angle. Subtracting the complementary angle from the supplementary angle, we have $90^{\circ}$ as $\frac{3}{4}$ of the supplementary angle. Thus the degree measure of the supplementary angle is $120^{\circ}$, and the degree measure of the desired angle is $180^{\circ} - 120^{\circ} = 60^{\circ}$. $\mathrm {(B)}$

列方程 $4(90-x)=(180-x)$。 $360-4x=180-x$ $3x=180$ 化简得 $x=60 \Rightarrow \mathrm {(B)}$ 由于余角是补角的 $\frac{1}{4}$。用补角减去余角，可得 $90^{\circ}$ 是补角的 $\frac{3}{4}$。因此补角的度数为 $120^{\circ}$，所求角的度数为 $180^{\circ} - 120^{\circ} = 60^{\circ}$。$\mathrm {(B)}$

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