75-25=50
50/75=0.6666666...
0.6666666...x100=66.666...
=66.7%
The person who answered already is correct
Answer:
The measures of angles of triangle MNP are
![M=[\gamma+\alpha-\beta]](https://tex.z-dn.net/?f=M%3D%5B%5Cgamma%2B%5Calpha-%5Cbeta%5D)
![N=[\beta+\alpha-\gamma]](https://tex.z-dn.net/?f=N%3D%5B%5Cbeta%2B%5Calpha-%5Cgamma%5D)
![P=[\beta+\gamma-\alpha]](https://tex.z-dn.net/?f=P%3D%5B%5Cbeta%2B%5Cgamma-%5Calpha%5D)
Step-by-step explanation:
step 1
Find the measure of arcs AB, BC and AC
we know that
The inscribed angle is half that of the arc it comprises.
so
----> ![arc\ AB=2\gamma](https://tex.z-dn.net/?f=arc%5C%20AB%3D2%5Cgamma)
----> ![arc\ BC=2\alpha](https://tex.z-dn.net/?f=arc%5C%20BC%3D2%5Calpha)
----> ![arc\ AC=2\beta](https://tex.z-dn.net/?f=arc%5C%20AC%3D2%5Cbeta)
step 2
Find the measure of angle M
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![M=\frac{1}{2}[arc\ AB+arc\ BC-arc\ AC]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AB%2Barc%5C%20BC-arc%5C%20AC%5D)
substitute
![M=\frac{1}{2}[2\gamma+2\alpha-2\beta]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cgamma%2B2%5Calpha-2%5Cbeta%5D)
![M=[\gamma+\alpha-\beta]](https://tex.z-dn.net/?f=M%3D%5B%5Cgamma%2B%5Calpha-%5Cbeta%5D)
step 3
Find the measure of angle N
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![N=\frac{1}{2}[arc\ AC+arc\ BC-arc\ AB]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20BC-arc%5C%20AB%5D)
substitute
![N=\frac{1}{2}[2\beta+2\alpha-2\gamma]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Calpha-2%5Cgamma%5D)
![N=[\beta+\alpha-\gamma]](https://tex.z-dn.net/?f=N%3D%5B%5Cbeta%2B%5Calpha-%5Cgamma%5D)
step 4
Find the measure of angle P
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
![P=\frac{1}{2}[arc\ AC+arc\ AB-arc\ BC]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%2Barc%5C%20AB-arc%5C%20BC%5D)
substitute
![P=\frac{1}{2}[2\beta+2\gamma-2\alpha]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Cgamma-2%5Calpha%5D)
![P=[\beta+\gamma-\alpha]](https://tex.z-dn.net/?f=P%3D%5B%5Cbeta%2B%5Cgamma-%5Calpha%5D)