Question

Луч ОС делит прямой угол АОB на два угла так,что угол АОС В 4 раза меньше угла ВОС . Найдите градусные меры углов АОС и ВОС

Answer 1

Угол 90 град. делим на 5 частей
90 : 5 = 18° - ∠АОС
18*4 = 72° - ∠ВОС

Answer 2

Problem Analysis

We are given that the angle AOB is divided by a line OC into two angles, where the angle AOC is four times smaller than the angle BOC. We need to find the measures of angles AOC and BOC.

Solution

Let's assume the measure of angle BOC is x degrees. According to the given information, the measure of angle AOC is four times smaller than angle BOC. Therefore, the measure of angle AOC is (1/4) * x degrees.

Since the sum of the measures of angles AOC and BOC is equal to the measure of angle AOB, we can write the equation:

(1/4) * x + x = 90

Simplifying the equation, we get:

(5/4) * x = 90

To solve for x, we can multiply both sides of the equation by (4/5):

x = (90 * 4) / 5

Calculating the value of x, we find:

x = 72

Therefore, the measure of angle BOC is 72 degrees.

To find the measure of angle AOC, we can substitute the value of x into the equation:

(1/4) * 72 = 18

Therefore, the measure of angle AOC is 18 degrees.

Answer

The measure of angle AOC is 18 degrees and the measure of angle BOC is 72 degrees.