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Triangle angle sum

Triangle angle sum theorem
The sum of the degree measures of the angles of a triangle is 180º.

aº + bº + cº = 180º

Proof:
In the following figure, line l has been drawn parallel to side AC of the triangle and through one of its vertices (B)

Since l||AC, alternate interior angles are equal in measure:

m<1 = m<4 and m<3 = m<5

The sum of the degree measures of the angles formed at vertex B is 180º:

m<4 + m<2 + m<5=180º

We may therefore substitute in the above equation m<1 for m<4 and m<3 for m<5:

m<1 + m<2 + m<3 = 180º

Find x and y:

Solution:

xº + 32º + 41º = 180º
xº + 73º = 180º
xº=107º

73º + 20º + yº =180º
93º + yº =180º
yº=87º

Find x:

Solution:

(2x-3) + (3x+8) + 5x = 180º
10x+5 = 180º
10x= 175º
x=17.5º