Difference between revisions of "2002 AMC 12A Problems/Problem 4"

(Solution 2)
(Solution 2)
 
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After simplifying, we get <math>x=60 \Rightarrow \mathrm {(B)}</math>
 
After simplifying, we get <math>x=60 \Rightarrow \mathrm {(B)}</math>
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=== Solution 2 ===
 
=== Solution 2 ===
  
Given that the complementary angle is <math>\frac{1}{4} of the supplementary angle. Subtracting the complementary angle from the supplementary angle, we have </math>90^{\circ}<math> as </math>\frac{3}{4}<math> of the supplementary angle.
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Given that the complementary angle is <math>\frac{1}{4}</math> of the supplementary angle. Subtracting the complementary angle from the supplementary angle, we have <math>90^{\circ}</math> as <math>\frac{3}{4}</math> of the supplementary angle.
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Thus the degree measure of the supplementary angle is <math>120^{\circ}</math>, and the degree measure of the desired angle is <math>180^{\circ} - 120^{\circ} = 60^{\circ}</math>. <math>\mathrm {(B)}</math>
  
Thus the degree measure of the supplementary angle is </math>120^{\circ}<math>, and the degree measure of the desired angle is </math>180^{\circ} - 120^{\circ} = 60^{\circ}<math>. </math>
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~ Nafer
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2002|ab=A|num-b=3|num-a=5}}
 
{{AMC12 box|year=2002|ab=A|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 18:14, 20 August 2019

Problem

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

$\mathrm{(A) \ 48 } \qquad \mathrm{(B) \ 60 } \qquad \mathrm{(C) \ 75 } \qquad \mathrm{(D) \ 120 } \qquad \mathrm{(E) \ 150 }$


Solution

Solution 1

We can create an equation for the question, $4(90-x)=(180-x)$

$360-4x=180-x$

$3x=180$

After simplifying, we get $x=60 \Rightarrow \mathrm {(B)}$


Solution 2

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 $180^{\circ} - 120^{\circ} = 60^{\circ}$. $\mathrm {(B)}$

~ Nafer

See Also

2002 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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