#UKMT 2023 Question

15 messages · Page 1 of 1 (latest)

fading violetBOT
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torpid rose
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The angle WTS can be easily seen when making a triangle out of the points WTS.

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(drawing a line WT)

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The triangle is isosceles, so SWT and WTS are equal

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To help find this angle, WST must be found.

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An angle sum of 360º is made up of WST, PST, PSR and WSR.

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PST = 60º as all angles are equal in an equilateral triangle.

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PSR = 90º as it is a right angle of a square.

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WSR = 108º as it is an angle of a regular pentagon. (angle sum 540/5)

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360-60-90-108 = WST = 102º

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This is an angle in the isosceles triangle made out of WST. The other two angles are equal to each other. The overall sum of this triangle is 180º.

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180-102 = 2WTS = 72º

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WTS = 36º

open terrace
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I will give you a hint
WS = ST so <SWT=<WTS