Answer: [tex]\angle{YXZ}=56^{\circ}[/tex]
Step-by-step explanation:
Given : ∠WXY and ∠YXZ are supplementary angles.
∠WXY= 8x+12 and ∠YXZ = 2x+28
We know that the pair of supplementary angles are added up to 180°.
According to the question, we have
[tex]\angle{WXY}+\angle{YXZ}=180^{\circ}\\\\\Rightarrow\ 8x+12+2x+28=180\\\\\Rightarrow\ 10x+40=180\\\\\Rightarrow\ 10x=180-40\\\\\Rightarrow\ 10x=140\\\\\Rightarrow\ x=\dfrac{140}{10}=14[/tex]
Now, [tex]\angle{YXZ}=2(14)+28=56^{\circ}[/tex]
Hence, the measure of [tex]\angle{YXZ}=56^{\circ}[/tex].
