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1 answer:
Answer:
m(∠y) = 64°
Step-by-step explanation:
From the figure attached,
m(∠e) = 90°
m(∠b) + 67° = 180° [Linear pair of angles]
m(∠b) = 180 - 67
= 113°
m(∠c) + 75° = 180° [Linear pair of angles]
m(∠c) = 105°
m(∠a) = m(∠d)
By the property of a polygon,
Sum of the interior angles of a polygon is given by,
Sum of interior angles = (n - 2) × 180°
Here, n = number of sides of the polygon
For n = 5,
Sum of interior angles = (5 - 2)×180°
= 540°
m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°
2m(∠d) + 113° + 105° + 90° = 540°
2m(∠d) + 308 = 540°
2m(∠d) = 540 - 308
m(∠d) = 116°
m(∠d) + m(∠y) = 180°
m(∠y) + 116° = 180° [Linear pair of angles]
m(∠y) = 64°
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The correct option which resembles with the given graph is .
Further explanation:
From the given graph the it is observed that the interval is which is a half open interval or it can be said that it is a half closed interval.
A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.
For example:
In an interval of the form the point
is included in the set but the point
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Similarly, in the interval the point
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is not included in the set.
In order to determine the correct option which resembles with given graph form interval for each option.
Option A:
As per the statement in option A the age of the student must be at least years and not more than
years that is the age of the student is either
years or greater than
years and less than
years.
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is not included which means it is a half closed or half opoen interval.
Therefore, is a correct option.
Option B:
As per the statement in option B the amount of money the babysitter can earn is between and
per hour.
As per the above statement the interval formed is in which both of the end points are not included in the set which means that it is an open interval.
Therefore, is an incorrect option.
Option C:
As per the statement in option C the time required to complete a program in college cannot be less than hours and the time must be less than
hours.
From the above statement it is concluded that the time required can be hours or more than
hours but it has to be less than
hours.
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Therefore, is a correct option.
Option D:
As per the statement in option D the age of the dogs is either years old or below
years and age of the dog must be greater than
tears.
As per the above statement the interval formed is .
Therefore, the is an incorrect option.
So, are the correct options which resembles with the given graph.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Sets
Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.