Question

Углы AOB и BOC -с межные, луч OD - бессектриса угла AOB, угодл BOD на 18° меньше угла BOC. Найдите углы AOB и BOC.

Answer 1

Точно ничeго нe пропущeно

Answer 2

Finding the Angles AOB and BOC

To find the angles AOB and BOC, we can use the information given in the question. Let's break down the problem step by step.

1. We are given that angles AOB and BOC are consecutive angles, meaning they share a common side and vertex. Let's call the common side OB.

2. We are also given that the ray OD is the angle bisector of angle AOB. This means that it divides angle AOB into two equal angles.

3. Additionally, we are told that angle BOD is 18° less than angle BOC.

Based on this information, we can proceed to find the values of angles AOB and BOC.

Solution:

Let's assume the measure of angle BOC is x degrees.

1. Since ray OD is the angle bisector of angle AOB, angle AOD is equal to angle BOD. Therefore, angle AOD is also x degrees.

2. We know that angle BOD is 18° less than angle BOC. So, angle BOD is (x - 18) degrees.

3. Since angles AOB and BOD are consecutive angles, their sum is 180°. Therefore, we can write the equation: AOB + BOD = 180°.

4. Substituting the values we have, we get: x + (x - 18) = 180°.

5. Simplifying the equation, we have: 2x - 18 = 180°.

6. Solving for x, we add 18 to both sides of the equation: 2x = 198°.

7. Dividing both sides by 2, we find: x = 99°.

Therefore, angle BOC is 99°, and angle AOB is (99 - 18) = 81°.

Answer:

The measure of angle AOB is 81°, and the measure of angle BOC is 99°.

Please let me know if there is anything else I can help you with!