Folded paper

Geometry Level 2

A piece of paper in the shape of an equilateral triangle has one corner folded over as shown.

What is the value of x x ?

  1. Diagram not drawn to scale
70 80 90 60 100

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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2 solutions

I will be using the following diagram to refer to the question:

The angles in red are 60° because it is an equilateral triangle {given in the question}

We can soon find out that a ° \color{#3D99F6} a° = 180 − 40 2 = 70 ° \dfrac{180 - 40}{2} = 70°

Therefore b ° \color{#20A900} b° = 180 − 70 − 60 = 50 ° 180 - 70 - 60 = 50°

Hence we can deduce that

x ° = 80 ° \large x° = 80°

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Jeremy Galvagni
Aug 2, 2018

Every angle in the pink pentagon is known except for x x . The interior angles in a pentagon add to 18 0 ∘ ( 5 − 2 ) = 54 0 ∘ 180^{\circ}(5-2)=540^{\circ}

54 0 ∘ − 30 0 ∘ − 4 0 ∘ − 6 0 ∘ − 6 0 ∘ = 80 ∘ 540^{\circ}-300^{\circ}-40^{\circ}-60^{\circ}-60^{\circ}=\boxed{80}^{\circ}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Hey Jeremy Galvagni, can you help me for the following:

https://brilliant.org/discussions/thread/some-problems-which-i-am-stuck-at-any-help-i-beg/

Syed Hamza Khalid - 2 years, 10 months ago

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