Colorful angles

Geometry Level 3

The red angle is smaller then the blue angle. What follows from this

A : The yellow angle is bigger then the green angle.

B : The yellow angle is smaller then the green angle.

C : Neither A nor B .

A B C

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Áron Bán-Szabó by Áron Bán-Szabó , 17, Hungary

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2 solutions

Uros Stojkovic
Jul 4, 2017

O r a n g e {\color{#EC7300} Orange} is obviously always bigger than C y a n {\color{cyan} Cyan} .

B l u e + G r e e n + O r a n g e = R e d + Y e l l o w + C y a n = 18 0 ∘ {\color{#3D99F6} Blue} + {\color{#20A900} Green} + {\color{#EC7300} Orange}= {\color{#D61F06} Red} + {\color{#CEBB00} Yellow}+ {\color{cyan} Cyan}=180^{\circ} and B l u e > R e d {\color{#3D99F6} Blue}> {\color{#D61F06} Red} , O r a n g e > C y a n {\color{#EC7300} Orange}> {\color{cyan} Cyan} .

Hence, Y e l l o w > G r e e n {\color{#CEBB00} Yellow}> {\color{#20A900} Green} .

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Nice solution, thanks!

Áron Bán-Szabó - 3 years, 11 months ago

You made a typo mistake: 360 has to be 180, please correct it!

Áron Bán-Szabó - 3 years, 11 months ago

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I've just corrected it, thank you!

Uros Stojkovic - 3 years, 11 months ago
Marta Reece
Jul 1, 2017

Sorry about G R E E N < R E D < B L U E < Y E L L O W \color{#20A900}GREEN<\color{#D61F06}RED<\color{#3D99F6}BLUE<\color{#CEBB00}YELLOW

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The segment in the triangle is not necessarily parallel to the below side of the triangle.

Áron Bán-Szabó - 3 years, 11 months ago

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