Problem Statement: Two supplementary angles differ by 34 degrees. Find the angles.

Solution:

Let's assume the two angles are 'a' and 'b', where 'a' is the larger angle and 'b' is the smaller angle.

We are given that the two angles are supplementary, which means that the sum of the angles is 180 degrees. So, we can write the equation as:

a + b = 180 ----(1)

We are also given that the two angles differ by 34 degrees. Mathematically, we can express this as:

a - b = 34 ----(2)

To find the values of 'a' and 'b', we can solve the system of equations (1) and (2).

Solving the System of Equations:

To solve the system of equations, we can use the method of substitution. We can solve equation (2) for 'a' in terms of 'b' and substitute it into equation (1).

From equation (2), we have:

a = b + 34

Substituting this value of 'a' into equation (1), we get:

(b + 34) + b = 180

Simplifying the equation:

2b + 34 = 180

Subtracting 34 from both sides:

2b = 180 - 34

2b = 146

Dividing both sides by 2:

b = 73

Now that we have the value of 'b', we can substitute it back into equation (2) to find 'a':

a - 73 = 34

Adding 73 to both sides:

a = 34 + 73

a = 107

Therefore, the two angles are 107 degrees and 73 degrees.