Answer:
[tex]m\angle WYX=20^{\circ}[/tex]
[tex]m\angle WYZ=70^{\circ}[/tex]
Step-by-step explanation:
We have been given that [tex]m\angle WYX=(4x-8)^{\circ}[/tex] and [tex]m\angle WYZ=(10x)^{\circ}[/tex].
Since ∠WYX and ∠WYZ are complementary, so they will add up-to 90 degrees.
[tex]m\angle WYZ+m\angle WYX=90^{\circ}[/tex]
Substitute the given values:
[tex]4x-8+10x=90[/tex]
Combine like terms:
[tex]14x-8=90[/tex]
[tex]14x-8+8=90+8[/tex]
[tex]14x=98[/tex]
[tex]\frac{14x}{14}=\frac{98}{14}[/tex]
[tex]x=7[/tex]
Let us substitute [tex]x=7[/tex] in measure of each angle as:
[tex]m\angle WYX=(4(7)-8)^{\circ}[/tex]
[tex]m\angle WYX=(28-8)^{\circ}[/tex]
[tex]m\angle WYX=20^{\circ}[/tex]
Therefore, the measure of angle WYX is 20 degrees.
[tex]m\angle WYZ=(10x)^{\circ}[/tex]
[tex]m\angle WYZ=(10(7))^{\circ}[/tex]
[tex]m\angle WYZ=70^{\circ}[/tex]
Therefore, the measure of angle WYZ is 70 degrees.
