Two angles of a triangle are equal and the third angle is greater than each one of them by 18 degree.Find the angles.
A1 = A2
Eq: A1 + A2 + A3 = 180o
A1 + A2 + (A1+18) = 180
Replace A2 with A1:
A1 + A1 + (A1+18) = 180
3A1 + 18 = 180
3A1 = 180-18 = 162
A1 = A2 = 54o
A3 = A1 + 18 = 54 + 18 = 72o.
To find the angles, let's break the problem down into steps:
Step 1: Identify the given information.
From the problem statement, we know that two angles of the triangle are equal, and the third angle is greater than each of them by 18 degrees.
Step 2: Assign variables to the unknown angles.
Let's assume the two equal angles are represented by 'x' degrees each and the third angle is represented by 'x + 18' degrees.
Step 3: Write an equation.
The sum of the three angles of a triangle is always 180 degrees. Therefore, we can write an equation:
x + x + (x + 18) = 180
Step 4: Solve the equation.
Combining like terms: 3x + 18 = 180
Subtracting 18 from both sides: 3x = 162
Dividing by 3: x = 54
Step 5: Calculate the angles.
Now plug the value of x back into the equation to find the angles:
The two equal angles are both 54 degrees, and the third angle is 54 + 18 = 72 degrees.
Therefore, the angles of the triangle are 54 degrees, 54 degrees, and 72 degrees.