let the two angles e represented by 'a' and 'b'. obtain two equations for each case, and then find the angles.
the angles are adjacent and form an angle measuring 75 degrees. their difference is 21 degrees.
To solve this problem, we need to set up two equations based on the given information and then solve for the angles 'a' and 'b'.
Let's break down the problem into two cases:
Case 1: The angles are adjacent and form an angle measuring 75 degrees.
In this case, the sum of the two angles is equal to 75 degrees.
Equation 1: a + b = 75
Case 2: The difference between the angles is 21 degrees.
In this case, one angle is 21 degrees larger than the other.
Equation 2: a - b = 21
Now, we have two equations:
a + b = 75 ---- (Equation 1)
a - b = 21 ---- (Equation 2)
We can solve this system of equations using any method, such as substitution or elimination.
Let's use the elimination method to solve for 'a' and 'b':
Add both equations:
(a + b) + (a - b) = 75 + 21
Simplifying the equation:
2a = 96
Divide both sides by 2:
a = 48
Now, substitute the value of 'a' into Equation 1:
48 + b = 75
Subtract 48 from both sides:
b = 75 - 48
b = 27
Therefore, the two angles 'a' and 'b' are:
a = 48 degrees
b = 27 degrees