Inside the unfolded angle AOB, the rays OC and OD are drawn so that the angle COD = 70 degrees

Inside the unfolded angle AOB, the rays OC and OD are drawn so that the angle COD = 70 degrees and the degree measures BOD and AOC are 2: 3, respectively. What is the degree measure of the angle AOC equal to?

The degree measure of the flattened angle is 180 °:

∠ AOB = 180 °.

This means that the sum of the angles AOC, COD and DOB is 180 °:

∠ AOC + ∠ COD + ∠ DOB = 180 °;

Let’s solve the problem using the equation, where:

2x – ∠ BOD;

3x – ∠ AOC;

Let’s compose and solve the equation:

∠ AOC + ∠ COD + ∠ DOB = 180 °;

3x + 70 + 2x = 180;

5x + 70 = 180;

5x = 180 – 70;

5x = 110;

x = 110/5;

x = 22;

3x = 3 * 22 = 66 ° – AOC angle.

Answer: 66 °