Introduction to triangle with 1 obtuse angle:
Let x be one of the angle in a triangle. If 90 < y < 180, then we can call x as an obtuse angle. The triangle with one angle obtuse angle, can be called as an obtuse angled triangle.
Now let us do few problems on this topic of triangle with 1 obtuse angle.
Example Problems on Triangle with 1 Obtuse Angles.
Ex 1: If the anlges of a triangle are 3y + 20, 2y + 5 and 2y – 20, Then check whether it will form an obtuse angled triangle.
Soln: Given: The angles are 3y + 20, 2y + 5, 2y – 20.
Sum of the angles of a triangle is 180˚.
Therefore (3y + 20) + (2y + 5) + (2y – 20) = 180
`=>` 7y + 25 – 20 = 180
`=>` 7y = 175
`=>` y = 25.
Therefore the angles are 3y + 20 = 3 (25) + 20 = 95
2y + 5 = 3 (25) + 5 = 55
2y – 20 = 2 (25) – 20 = 30
Since one of the angle 95˚ is more than 90˚, the given angles will form an obtuse angled triangle.
Ex 2: In an obtused angle triangle, the obtuse angle is 120˚. The other two angles are given by y + 10 and 2y + 5. Find the angles.
Soln: Since one of the angle is 120˚.
Then (y + 10) + (2y + 15) = 180 – 120 = 60˚
Therefore 3y + 15 = 60
`=>` 3y = 45
`=>` y = 15.
Therefore the angles are 15 + 10, 2 (15) + 15
= 25˚ and 45˚.
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More Example Problems on Triangle with 1 Obtuse Angles.
Ex 3: Let triangle be formed by the following three angles: 5y + 10, 2y + 5 and y + 5. Find the obtuse angle.
Soln: Given: The angles of a triangle are 5y + 10, 2y + 5 and y + 5
Therefore (5y + 10) + (2y + 5 ) + (y + 5) = 180
8y + 20 = 180
`=>` y = `160 / 8` = 20.
Therefore the obtuse angle is 5y + 10 = 5 (20) + 10 = 110˚.
Ex 4: The difference of an obtuse angle and the smallest angle in the triangle is 80. The difference between the obtuse angle and the other angle is 55˚. Find the obtuse angle.
Soln: Let y be the obtuse angle. Let x and z be the smallest and the other angle respectively.
Given: y – x = 80 …………….. (1)
y – z = 55 …………….. (2)
x + y + z = 180 ………… (3)
(1) `=>` x = y – 80,
(2)`=>` z = y – 55,
Therefore (3)`=>` y – 80 + y + y – 55 = 180
Therefore y = 105.
Hence the obtuse angle is 1050.
Let x be one of the angle in a triangle. If 90 < y < 180, then we can call x as an obtuse angle. The triangle with one angle obtuse angle, can be called as an obtuse angled triangle.
Now let us do few problems on this topic of triangle with 1 obtuse angle.
Example Problems on Triangle with 1 Obtuse Angles.
Ex 1: If the anlges of a triangle are 3y + 20, 2y + 5 and 2y – 20, Then check whether it will form an obtuse angled triangle.
Soln: Given: The angles are 3y + 20, 2y + 5, 2y – 20.
Sum of the angles of a triangle is 180˚.
Therefore (3y + 20) + (2y + 5) + (2y – 20) = 180
`=>` 7y + 25 – 20 = 180
`=>` 7y = 175
`=>` y = 25.
Therefore the angles are 3y + 20 = 3 (25) + 20 = 95
2y + 5 = 3 (25) + 5 = 55
2y – 20 = 2 (25) – 20 = 30
Since one of the angle 95˚ is more than 90˚, the given angles will form an obtuse angled triangle.
Ex 2: In an obtused angle triangle, the obtuse angle is 120˚. The other two angles are given by y + 10 and 2y + 5. Find the angles.
Soln: Since one of the angle is 120˚.
Then (y + 10) + (2y + 15) = 180 – 120 = 60˚
Therefore 3y + 15 = 60
`=>` 3y = 45
`=>` y = 15.
Therefore the angles are 15 + 10, 2 (15) + 15
= 25˚ and 45˚.
Please express your views of this topic triangle area by commenting on blog.
More Example Problems on Triangle with 1 Obtuse Angles.
Ex 3: Let triangle be formed by the following three angles: 5y + 10, 2y + 5 and y + 5. Find the obtuse angle.
Soln: Given: The angles of a triangle are 5y + 10, 2y + 5 and y + 5
Therefore (5y + 10) + (2y + 5 ) + (y + 5) = 180
8y + 20 = 180
`=>` y = `160 / 8` = 20.
Therefore the obtuse angle is 5y + 10 = 5 (20) + 10 = 110˚.
Ex 4: The difference of an obtuse angle and the smallest angle in the triangle is 80. The difference between the obtuse angle and the other angle is 55˚. Find the obtuse angle.
Soln: Let y be the obtuse angle. Let x and z be the smallest and the other angle respectively.
Given: y – x = 80 …………….. (1)
y – z = 55 …………….. (2)
x + y + z = 180 ………… (3)
(1) `=>` x = y – 80,
(2)`=>` z = y – 55,
Therefore (3)`=>` y – 80 + y + y – 55 = 180
Therefore y = 105.
Hence the obtuse angle is 1050.
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