Question

The circle is divided into 360 equal parts. Point A represents the center of the circle. The measure of angle

Answer 1

Answer:

$\angle XYZ= 15^\circ$

Step-by-step explanation:

Given

$\theta = 360^\circ$

See attachment for complete question

Required

Determine the measure of $\angle XYZ$

From the attachment, we have:

$XT = 180$ --- Semi circle

$\angle TAR = 90$ --- Quadrant

$\angle RAZ = 75$

Since all the angles add up to 360 degrees, we have:

$XT + \angle TAR + \angle RAZ + \angle XYZ= \theta$

This gives:

$180 + 90 + 75 +\angle XYZ= 360$

$345 +\angle XYZ= 360$

Collect like terms

$\angle XYZ= -345 + 360$

$\angle XYZ= 15^\circ$