Answer:85
Step-by-step explanation:
Answer:
The measure of the
is ![80^{\circ}](https://tex.z-dn.net/?f=80%5E%7B%5Ccirc%7D)
Step-by-step explanation:
We know that the measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.
Now, Let
x is the measure of arc IV
and y is the measure of arc PK, then
![m{\angle}ISV={\frac{1}{2}}(x+y)](https://tex.z-dn.net/?f=m%7B%5Cangle%7DISV%3D%7B%5Cfrac%7B1%7D%7B2%7D%7D%28x%2By%29)
Substituting the given values, we get
![135^{\circ}={\frac{1}{2}(140^{\circ}+y)](https://tex.z-dn.net/?f=135%5E%7B%5Ccirc%7D%3D%7B%5Cfrac%7B1%7D%7B2%7D%28140%5E%7B%5Ccirc%7D%2By%29)
![270^{\circ}=140^{\circ}+y](https://tex.z-dn.net/?f=270%5E%7B%5Ccirc%7D%3D140%5E%7B%5Ccirc%7D%2By)
![y=130^{\circ}](https://tex.z-dn.net/?f=y%3D130%5E%7B%5Ccirc%7D)
Thus, The measure of arc PK is
.
Also, we know that the inscribed angle measures half that of the arc comprising
, thus
Let
z is the measure of arc VK
and y is the measure of arc PK, then
![m{\angle}VPL={\frac{1}{2}(z+y)](https://tex.z-dn.net/?f=m%7B%5Cangle%7DVPL%3D%7B%5Cfrac%7B1%7D%7B2%7D%28z%2By%29)
Substituting the values, we get
![m{\angle}VPL={\frac{1}{2}}(30+130)=80^{\circ}](https://tex.z-dn.net/?f=m%7B%5Cangle%7DVPL%3D%7B%5Cfrac%7B1%7D%7B2%7D%7D%2830%2B130%29%3D80%5E%7B%5Ccirc%7D)
Hence, the measure of the
is
.
Answer:
4x - 2y = -12
Step-by-step explanation:
4(3) - 2(12) = b
12 - 24 = b
-12 = b
4x-2y = -12