Answer:
3). [tex]x=105[/tex]
4). [tex]x=21[/tex]
Step-by-step explanation:
We have been given two circles, we are asked to find the value of x for each circle.
3) We know that measure of inscribed angle is half the measure of intercepted arc. Since the measure of angle ACB is x degrees, so measure of arc AB will be 2x degrees.
The measure of arc ACB is [tex](x+45)^{\circ}[/tex]. We know that circumference of circle is 360 degrees. We can set an equation as:
[tex]x+45+2x=360[/tex]
[tex]3x+45=360[/tex]
[tex]3x+45-45=360-45[/tex]
[tex]3x=315[/tex]
[tex]\frac{3x}{3}=\frac{315}{3}[/tex]
[tex]x=105[/tex]
Therefore, the value of x is 105.
4) We know that the measure of two inscribed angles corresponding to same arc is equal.
Since angle WXZ and WYZ corresponds to arc WZ, so we can set an equation as:
[tex]3x-40=x+2[/tex]
[tex]3x-x-40=x-x+2[/tex]
[tex]2x-40=2[/tex]
[tex]2x-40+40=2+40[/tex]
[tex]2x=42[/tex]
[tex]\frac{2x}{2}=\frac{42}{2}[/tex]
[tex]x=21[/tex]
Therefore, value of x is 21.
