# The ACB angle of 155 ° is divided into two angles by the CE beam. The degree measure of one of them is 25

The ACB angle of 155 ° is divided into two angles by the CE beam. The degree measure of one of them is 25 ° less than the degree measure of the other. Calculate the degree measures of the resulting angles.

The CE beam divides ∠ACB of 155 ° into two angles ∠ACE and ∠BCE:
∠ACE + ∠BCE = ∠ACB;
∠ACE + ∠BCE = 155 °.
Let’s denote ∠ACE as x, then ∠BCE, which is 25 ° less than ∠ACE (by condition), will be equal to x – 25 °.
Thus, we get a linear equation with one variable:
x + (x – 25 °) = 155 °;
x + x – 25 ° = 155 °;
2 * x = 155 ° + 25 °;
2 * x = 180 °;
x = 180 ° / 2;
x = 90 °.
Hence, ∠ACE = x = 90 °. Therefore, ∠BCE = x – 25 ° = 90 ° – 25 ° = 65 °.
Answer: ∠ACE is 90 °, ∠BCE is 65 °.

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