To solve the problem (assuming the common scenario where the difference between two angles is 15° and the sum of their complements is 75°), follow these steps:
Step 1: Define Variables
Let the two angles be (x) and (y) ((x > y)).
Given:
- Difference between angles: (x - y = 15^\circ)
- Sum of their complements: ((90^\circ - x) + (90^\circ - y) = 75^\circ)
Step 2: Simplify the Second Equation
((90 - x) + (90 - y) = 75)
(180 - (x + y) = 75)
(x + y = 180 - 75 = 105^\circ)
Step 3: Solve the System of Equations
We have:
[
\begin{cases}
x - y = 15 \
x + y = 105
\end{cases}
]
Add the two equations:
(2x = 120 \implies x = 60^\circ)
Substitute (x = 60^\circ) into (x + y = 105^\circ):
(60 + y = 105 \implies y = 45^\circ)
Answer: The two angles are (\boxed{60^\circ}) and (\boxed{45^\circ}). (If only one answer is needed, depending on context, but typically both are required.)
Assuming the question asks for the larger angle, the answer is (\boxed{60}).
(\boxed{60})
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