help please

Question

0

1

533

1

Three squares are joined together as shown in figure to create a triangle.

What is the sum of angles ∠A+∠B+∠C ?

Note: We are referring to the "exterior angles", not the interior angles of the triangle.

Guest Jun 30, 2020

geno3141 · Answer 1 · 2020-06-30T08:26:14

Let the three interior angles of the triangle be A', B', and C'

Then, A = 360^o - 90^o - 90^o - A' = 180^o - A'.

B = 360^o - 90^o - 90^o - B' = 180^o - B'.

C = 360^o - 90^o - 90^o - C' = 180^o - C'.

A + B + C = ( 180^o - A' ) + ( 180^o - B' ) + ( 180^o - C' ) = 540^o - A' - B' - C' = 540^o - ( A' + B' + C' )

= 540^o - 180^o = 360^o