Answer:
[tex]\angle XYZ= 15^\circ[/tex]
Step-by-step explanation:
Given
[tex]\theta = 360^\circ[/tex]
See attachment for complete question
Required
Determine the measure of [tex]\angle XYZ[/tex]
From the attachment, we have:
[tex]XT = 180[/tex] --- Semi circle
[tex]\angle TAR = 90[/tex] --- Quadrant
[tex]\angle RAZ = 75[/tex]
Since all the angles add up to 360 degrees, we have:
[tex]XT + \angle TAR + \angle RAZ + \angle XYZ= \theta[/tex]
This gives:
[tex]180 + 90 + 75 +\angle XYZ= 360[/tex]
[tex]345 +\angle XYZ= 360[/tex]
Collect like terms
[tex]\angle XYZ= -345 + 360[/tex]
[tex]\angle XYZ= 15^\circ[/tex]
