Respuesta :

Answer:

[tex]m\angle{W} = {75{^\circ}}[/tex]

[tex]m\angle{Y} = {15{^\circ}}[/tex]

[tex]m\angle{Z} = {90{^\circ}}[/tex]

Step-by-step explanation:

All angles in a triangle must add up to [tex]180{^\circ}[/tex]

First we can use an equation to find [tex]x[/tex]

[tex](x - 15) + (2x - 165) + 90 = 180[/tex]

[tex]3x - 180 = 90[/tex]

[tex]3x = 270[/tex]

[tex]x = 90[/tex]

Now we can solve for [tex]\angle W[/tex]and [tex]\angle Y[/tex] through substitution

[tex]\angle{W} = 90 - 15 \rightarrow \boxed{75{^\circ}}[/tex]

[tex]\angle{Y} = 2x - 165 \rightarrow 2(90) - 165 \rightarrow 180 - 165 \rightarrow \boxed{15{^\circ}}[/tex]

Now we can classify the triangle

It is right because it has a [tex]90{^\circ}[/tex] angle

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