Answer:
[tex]x=86^{\circ}[/tex]
[tex]y=94^{\circ}[/tex]
[tex]z=54^{\circ}[/tex]
Step-by-step explanation:
First, let's look at the largest triangle (two smaller triangles are combined) to solve for [tex]z[/tex]. Since the sum of the angles in a triangle adds up to [tex]180^{\circ}[/tex], we can write the equation:
[tex]20+74+32+z=180[/tex]
[tex]z=180-126[/tex]
[tex]z=54^{\circ}[/tex]
Looking at the smaller triangle on the left, [tex]y[/tex] (exterior angle) is the sum of the two opposite interior angles of the triangle on the left:
[tex]y=74+20[/tex]
[tex]=94^{\circ}[/tex]
Since [tex]x[/tex] is the exterior angle of the triangle on the right, it is equivalent to the sum of the opposite interior angles of that triangle:
[tex]x=32+z[/tex]
[tex]=32+54[/tex]
[tex]=86^{\circ}[/tex]
Hope this helps :)
