Question

Математика, 5 класс. Дидактические материалы. А.Г. Мерзляк, В.Б. Полонский и тд. Задание №508. Из вершины прямого угла AED проведены два луча EC и EF так, что угол AEF=58 градусов, угол CED=49 градусов. Вычислите величину угла CEF. Помогите, пожалуйста, разобраться, не получается решения. Спасибо))

Answer 1

Ответ: 17°

∠FED=90-58=32°
∠ CEF=49-32=17°

Answer 2

I'm sorry, but I am unable to browse the internet or access specific textbooks like "Mathematics, 5th grade" by A.G. Merzlyak and V.B. Polonsky. However, I can help you understand how to solve the problem you mentioned.

In the problem, we are given that two rays, EC and EF, are drawn from the vertex of a right angle AED. The angle AEF is 58 degrees, and the angle CED is 49 degrees. We need to find the measure of angle CEF.

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees. Since triangle CEF is a part of triangle AEF, we can find the measure of angle CEF by subtracting the measures of angles AEF and CED from 180 degrees.

Let's calculate the measure of angle CEF step by step:

1. Find the measure of angle AEC: - Since angle AED is a right angle, angle AEC is also a right angle (90 degrees).

2. Find the measure of angle AEF: - Given: angle AEF = 58 degrees.

3. Find the measure of angle CED: - Given: angle CED = 49 degrees.

4. Find the measure of angle CEF: - Subtract the measures of angles AEF and CED from 180 degrees: angle CEF = 180 degrees - angle AEF - angle CED.

Now, let's calculate the measure of angle CEF using the given values:

angle CEF = 180 degrees - 58 degrees - 49 degrees.

After performing the calculation, we find that the measure of angle CEF is 73 degrees.

I hope this helps! Let me know if you have any further questions.