In a triangle, the sum of two angles is equal to the third angle.If the difference between these two angles is 30 degree,Find the angles of the triangle.
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The angles of triangle are 60°, 30° and 90°.
Given - Sum and difference between two angles
Find - Angles of triangle
Solution - Let the three angles of triangle be a, b and c. Let the two angles be a and b.
a + b + c = 180 - Equation 1
a + b = c - Equation 2
Keep the value of c from Equation 2 in Equation 1
a + b + a + b = 180
2a + 2b = 180
2(a + b) = 180
a + b = 180/2
a + b = 90 - Equation 3
Now, representing the difference between the two angles
a - b = 30 - Equation 4
Now, adding Equation 3 and Equation 4
a + b = 90
a - b = 30
(On addition, b will be cancelled)
2a = 120
a = 120/2
a = 60
Keep the value of a in Equation 4 to find b.
b = a - 30
b = 60 - 30
b = 30
Finding value of angle c from Equation 1
60 + 30 + c = 180
90 + c = 180
c = 180 - 90
c = 90°
So, the angles of triangle are 60°, 30° and 90°.
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