A square and an isosceles triangle. Could you find the value of x?

Geometry, Polynomial expressions, sum of squares, algebra, algebraic equations, substitution, Challenging Math Problems, polynomial equations, algebra challenge, algebraic identities, algebraic challenge.

[satyanarayanmohanty]

Sir, without using inscribed angle technique and applying isosceles triangle concept in bot isosceles triangles we can easily calculate x=45. 90-y+x+y+x=180=>x=45.

[HassanLakiss]

Thank you for a nice question and clearly demonstrated solution.

[harikatragadda]

Draw a diagonal of the Square from left to right. This diagonal is a chord that subtends 90° at the centre O of the Circle, and subtends half of it on the circumference, at the left corner of the triangle. Hence x=45°.

[ATULibrary]

Nice video from Obed - Accra Technical University Library

[danielettedgui]

The first proof is very confusing. How does rotating the vertex get you to x= 45 degrees? Other proof is excellent.