Question

Луч CE делит развёрнутый угол ACB на два угла так, что ∠ACE = 150°, а ∠ECB = 30°. Точка D принадлежит углу ECB и градусная мера ∠ACD равна 168°. Вычислите градусную меру ∠DCB и ∠ECD. Выполните рисунок и запишите подробное решение с пояснениями.

Answer 1

Ответ:

<DCB=12°, <ECD=18°

Пошаговое объяснение:

На фотографии

Answer 2

Problem Analysis

We are given an angle ACB, which is divided into two angles by a line CE. The measure of angle ACE is 150°, and the measure of angle ECB is 30°. Point D lies within angle ECB, and the measure of angle ACD is 168°. We need to find the measures of angles DCB and ECD.

Solution

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180°. We can start by finding the measure of angle AEC.

Since angle ACE is 150° and angle ECB is 30°, the measure of angle AEC is the sum of these two angles: 150° + 30° = 180°.

Now, we can find the measure of angle ECD. Since the sum of the angles in triangle AEC is 180°, we can subtract the measures of angles ACE and ACD from 180° to find the measure of angle ECD.

The measure of angle ACE is 150°, and the measure of angle ACD is 168°. Subtracting these angles from 180° gives us: 180° - 150° - 168° = -138°.

However, angles cannot have negative measures, so we need to adjust the measure of angle ECD. We can do this by adding 180° to -138°, which gives us: -138° + 180° = 42°.

Therefore, the measure of angle ECD is 42°.

To find the measure of angle DCB, we can subtract the measure of angle ECD from the measure of angle ECB. The measure of angle ECB is 30°, and the measure of angle ECD is 42°. Subtracting these angles gives us: 30° - 42° = -12°.

Again, angles cannot have negative measures, so we need to adjust the measure of angle DCB. We can do this by adding 180° to -12°, which gives us: -12° + 180° = 168°.

Therefore, the measure of angle DCB is 168°.

Summary

In summary, the measure of angle DCB is 168° and the measure of angle ECD is 42°.