In my Project Maths book (Text and Tests 2 Junior Cert Higher Level Maths) there is a question (pg 174 question 6 (c)) that shows a triangle and tells you to explain why the angle ABC is 90 degrees by marking equal angles. Could someone please explain how to do it? (I have attached a picture of the question) Thank you!

Hiphop
Hi, so you just need to work with the bigger triangle! (triangleABC)
First label the angles:
∠CAB = ∠1
∠ABX = ∠2
∠XBC = ∠3
∠ACB = ∠4
We know:
∠1 + ∠2 + ∠3 + ∠4 = 180°
∠1 = ∠2
∠3 = ∠4
Therefore,
∠2 + ∠2 + ∠4 + ∠4 = 180°
∠2 + ∠4 = 90°
:)

Ingo
Thanks so much!! I think I was confusing myself by overthinking. Thank you! :)

Hiphop
No problem!! :)

Me
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