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An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is
- a)37(1º/2)
- b)52(1º/2)
- c)72(1º/2)
- d)75º
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
An exterior angle of a triangle is 105° and its two interior oppos...
Given:
Exterior angle = 105° and two interior opposite angles are equal.
The concept used: The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Let the two interior angles be a and b be x°.
As given, d is the exterior angle i.e 105°.
d = a + b
105° = x° + x°
2x° = 105
x = 105/2
Exterior angle = 105° and two interior opposite angles are equal.
The concept used: The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Let the two interior angles be a and b be x°.
As given, d is the exterior angle i.e 105°.
d = a + b
105° = x° + x°
2x° = 105
x = 105/2
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Community Answer
An exterior angle of a triangle is 105° and its two interior oppos...
If an exterior angle of a triangle is 105 degrees, it means that this angle is formed by extending one side of the triangle. The sum of the interior angles of any triangle is always 180 degrees.
Therefore, the exterior angle is equal to the sum of the two opposite interior angles. Let's call the interior angles x and y.
According to the given information, we have:
105 = x + y
Since the sum of the interior angles is always 180 degrees, we can write another equation:
x + y = 180
Now we have a system of equations:
105 = x + y
x + y = 180
To solve this system, we can subtract the second equation from the first equation:
105 - (x + y) = 180 - (x + y)
105 - 180 = x + y - (x + y)
-75 = 0
This leads to a contradiction, which means that there is no solution for the given system of equations. Therefore, it is not possible for an exterior angle of a triangle to be 105 degrees.
Therefore, the exterior angle is equal to the sum of the two opposite interior angles. Let's call the interior angles x and y.
According to the given information, we have:
105 = x + y
Since the sum of the interior angles is always 180 degrees, we can write another equation:
x + y = 180
Now we have a system of equations:
105 = x + y
x + y = 180
To solve this system, we can subtract the second equation from the first equation:
105 - (x + y) = 180 - (x + y)
105 - 180 = x + y - (x + y)
-75 = 0
This leads to a contradiction, which means that there is no solution for the given system of equations. Therefore, it is not possible for an exterior angle of a triangle to be 105 degrees.
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An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles isa)37(1º/2)b)52(1º/2)c)72(1º/2)d)75ºCorrect answer is option 'B'. Can you explain this answer?
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