Answer:
B. 38°
Step-by-step explanation:
The angles of a triangle add up to 180.
So, 62 + 80 + b will add up to 180.
First, we add 62 =80, which gives us 142.
The we subtract 142 from 180, which gives us 38.
<h3>
Answer: x = 19</h3>
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Explanation:
Arc XPZ = 271 is shown in the diagram below as the blue arc. The red arc is the remaining bit minor arc XZ. The term "minor arc" refers to any arc that is less than 180 degrees.
Subtract the measure of arc XPZ from 360 to get
360 - (arc XPZ) = 360 - 271 = 89
So minor arc XZ is 89 degrees. Central angle ZCX is also 89 degrees because this central angle cuts off (or subtends) minor arc XZ.
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We are told that angle XYZ circumscribes the circle. This is just another way of saying that segments XY and YZ are tangent to the circle. Tangent segments form 90 degree angles with the radius. Therefore, angles CXY and CZY are both 90. I have marked both angles with square angle markers in the diagram below.
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We know three angles of quadrilateral CXYZ.
- angle ZCX = 89
- angle CXY = 90
- angle CZY = 90
The only thing we don't know is angle XYZ, which we'll just call some variable for now. Let's use M. So M = measure of angle XYZ.
For any quadrilateral, the four angles always add up to 360 degrees
(angleZCX)+(angleCXY)+(angleCZY)+(angleXYZ) = 360
89+90+90+M = 360
269+M = 360
269+M-269 = 360-269
M = 91
angle XYZ = 91 degrees
Set this equal to (4x+15), which is what angle XYZ is also equal to, then solve for x
4x+15 = 91
4x+15-15 = 91-15
4x = 76
4x/4 = 76/4
<h3>x = 19</h3>
Slope is -1
Y intercept is 2
9514 1404 393
Answer:
one solution; (x, y) = (4/3, 11/3)
Step-by-step explanation:
The two lines described by the equations have different slopes, so there will be exactly one solution to the system of equations.
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The slope of the line will be the coefficient of x when you solve for y. In the first equation, the slope is 2. In the second equation, you can solve for y by adding x, and dividing by 2. Then the slope of that line is found to be 1/2.
Lines with different slopes must intersect somewhere. That point of intersection is the (one) solution to the system of equations.