Sure, let's solve this step-by-step.
We need to find two angles, let's call them [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
1. We are given that the sum of the two angles is [tex]\( 85^\circ \)[/tex]. This is our first equation:
[tex]\[
A + B = 85
\][/tex]
2. We are also given that the difference between the two angles is [tex]\( 25^\circ \)[/tex]. This is our second equation:
[tex]\[
A - B = 25
\][/tex]
To find the value of [tex]\( A \)[/tex], we can add these two equations together:
[tex]\[
(A + B) + (A - B) = 85 + 25
\][/tex]
This simplifies to:
[tex]\[
2A = 110
\][/tex]
Now, solving for [tex]\( A \)[/tex]:
[tex]\[
A = \frac{110}{2} = 55
\][/tex]
Next, we use the value of [tex]\( A \)[/tex] to find [tex]\( B \)[/tex]. Subtract the second equation from the first equation:
[tex]\[
(A + B) - (A - B) = 85 - 25
\][/tex]
This simplifies to:
[tex]\[
2B = 60
\][/tex]
Now, solving for [tex]\( B \)[/tex]:
[tex]\[
B = \frac{60}{2} = 30
\][/tex]
Therefore, the two angles are:
[tex]\[
A = 55^\circ \quad \text{and} \quad B = 30^\circ
\][/tex]
