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

August 22, 2021 | education

| **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 °.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.