Question

Keep getting this one incorrect, don't know where i'm messing up at!

Answer 1

Answer:   x = 19

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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

x = 19