intersecting chord thereom?

Question

anonymous · Answer

attachment

directrix · Answer

Take a look at the attached theorem.
It tells you how to get the measure of an angle formed by two intersecting chords.

directrix · Answer

m<XYZ = (1/2) * (m arc XZ + m arc VW)

but ...

directrix · Answer

... we don't know the measures of arc XZ and VW.

So, let's get the measure of angle XYV.

anonymous · Answer

so the answer to that would be 108?

directrix · Answer

I don't know yet.

m< XYV = (1/2) * (m arc VX + m arc ZW)

m<XYV = (1/2)* (64 + 152)

@inm17 --> What is the value of (1/2)* (64 + 152)?

directrix · Answer

>> so the answer to that would be 108?   NO, that is not correct.

directrix · Answer

Just a second. I think I misread the problem.

directrix · Answer

False alarm. We are looking for angle XYZ.  We cannot get it directly.
So, we are first finding the measure of angle XYV which is (1/2)* (64 + 152) = 108.

But, 108 is not the measure of angle XYZ.  108 is the measure of the supplement of angle XYZ.

directrix · Answer

@inm17 What is the supplement of an angle of measure 108?