The Angly kid :0

Geometry Level 2

Adrian went to get his face pierced .He was having a great day until the piecer asked him a weird question (that made him angry) and told him that he will only continue after getting a correct answer.

Angly Adrian Angly Adrian

The question is as follows :

What is the sum of all the angles of your face?? ( marked ones ) \textcolor{#D61F06}{\text{What is the sum of all the angles of your face??}}\tiny{(\text{marked ones})}

Adrian is an emo and not so good at math .Being his frmd and good at math ,can you help him find the correct answer?

∞ ∞ 360° 1080° 1800° 720° 1440°

Agent T by Agent T , 17, India

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3 solutions

Agent T
May 16, 2021

The sum of interior angles of a n-gon is given by the formula:

n ∗ 180 = 360 − s u m \textcolor{#D61F06}{\boxed{\textcolor{#3D99F6}{n*180=360-sum}}}

There are 8 sides in this case ,so

8 ∗ 180 − 360 = s u m 8*180-360=sum

4 ∗ 360 − 360 = s u m 4*360-360=sum

360 ( 4 − 1 ) = s u m 360(4-1)=sum

360 ∗ 3 = s u m 360*3=sum

= > s u m = 1080 ° =>sum=1080°

Boom!

4 Helpful 2 Interesting 3 Brilliant 0 Confused
Ill Banin
Jun 1, 2021

Octagonal is 135×8 = 1080°, so answer is 1080°.

1 Helpful 1 Interesting 1 Brilliant 0 Confused

Noice work!!

Agent T - 1 week, 4 days ago
David Stiff
May 20, 2021

The sum of the angles in a triangle is 180 ° 180\degree . We can break up his face into four triangles. However, there are two extra 180 ° 180\degree angles to account for (labelled in the picture). Thus the sum of the angles is 6 × 180 ° = 1080 ° 6 \times 180\degree = \boxed{1080\degree}

1 Helpful 1 Interesting 1 Brilliant 0 Confused

You actually derived the formula for an eight sided polygon !! Great work!!

Agent T - 3 weeks, 1 day ago

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