UKMT Special (Problem $9$ )

The diagram shows $4$ identical white triangles symmetrically placed on a grey square. Each triangle is isosceles and right-angled. The total area of the visible grey regions is equal to the total area of the white triangles.

What is the smallest angle in each of the (identical) grey triangles in the diagram?

[UKMT Hamilton Olympiad $2015$ , H $6$ ]

#Geometry

Easy Math Editor

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`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

You have until this Sunday, $3:00$ pm!

Yajat Shamji - 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

UKMT Special (Problem 999)

Comments

UKMT Special (Problem $9$ )