Answer:
The measures of angles of triangle MNP are
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
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
![\gamma=\frac{1}{2}[arc\ AB] ----> arc\ AB=2\gamma\\\alpha=\frac{1}{2}[arc\ BC] ----> arc\ BC=2\alpha\\\beta=\frac{1}{2}[arc\ AC] ----> arc\ AC=2\beta](https://tex.z-dn.net/?f=%5Cgamma%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AB%5D%20----%3E%20arc%5C%20AB%3D2%5Cgamma%5C%5C%5Calpha%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20BC%5D%20----%3E%20arc%5C%20BC%3D2%5Calpha%5C%5C%5Cbeta%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20AC%5D%20----%3E%20arc%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]\\M=[\gamma+\alpha-\beta]](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cgamma%2B2%5Calpha-2%5Cbeta%5D%5C%5CM%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]\\N=[\beta+\alpha-\gamma]](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Calpha-2%5Cgamma%5D%5C%5CN%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]\\P=[\beta+\gamma-\alpha]](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B1%7D%7B2%7D%5B2%5Cbeta%2B2%5Cgamma-2%5Calpha%5D%5C%5CP%3D%5B%5Cbeta%2B%5Cgamma-%5Calpha%5D)
Answer:
Angle X=30°
2x=60°
Step-by-step explanation:
X+2X=90°
3x=90°
X=90/3
X=30°
Angle X=30°
2x=60°
Answer:
68 823 620
Step-by-step explanation:
if the last no. is 5 or above add 1 to the number after it and turn the original number into zero but if the last no. if below or 4 then keep it as it is and change the last no. to zero
Answer:
x=12 and y=1
to find the x value, you multiply the y value by 2.
6×2=12
to find y, you divide x by 2.
2/2=1
Answer:
Area = 5x^2 +7x -26
Step-by-step explanation:
The area of the shaded region can be found if you substruct the small rectangle from the big one. The area of any rectangle is calculated if you multiply width and height.
In other words:
A_small = (x-3)(x-6) = x^2-9x +18
A_big = (2x+2)(3x-4) = 6x^2 -2x -8
A_big - A_small = (6x^2 -2x -8) - (x^2-9x +18)
= 6x^2 -2x -8 - x^2 + 9x -18
= 5x^2 +7x -26
