Use the segment addition postulate to write three equations using the diagram below
1 answer:
Answer:
=> equation 1
=> equation 2
=> equation 3
Step-by-step explanation:
Points P, Q, R, S, and T are collinear therefore, the following equations can be written based on the segment addition postulate:
=> equation 1
=> equation 2
=> equation 3
More equations can actually be written from the diagram given using the segment addition postulate. Such as:
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If the measure of central angle is 3π /4 radians, then the area off the shaded sector is 96π square units
The radius of the circle = 16 units
The central angle of the shaded region = 3π /4 radians
The area of the sector = (θ/ 360) × πr^2
Where θ is the central angle of the sector
r is the radius of the sector
Substitute the values in the equation
The area of the sector = ((3π /4) /360) × π × 16^2
Convert the radians to the degrees
= (135/360) × 256π
Multiply the terms
= 96π square units
Hence, the area of the shaded sector is 96π square units
The complete question is
The measure of central angle XYZ is 3 pie / 4 radians. What is the area of the shaded sector?
Learn more about area of the sector here
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