Question

Rays OA , OB , OC and OD intersect each other and point O. Angle AOB is right angle and given that angle COD is 30° greater than BOC. Find m∠COD if m∠AOD = 210°.

Answer 1

To find the measure of ∠COD, we use the fact that the sum of all angles around point O is 360°. By subtracting known angles and setting up an equation, we find that ∠COD is 45°.

Step-by-step explanation:

To find the measure of ∠COD, we start by recognizing that the sum of angles around point O is 360° because they form a complete circle. Given that ∠AOD is 210° and ∠AOB is a right angle, ∠AOB is 90°. The remaining angle at point O is therefore 360° - 210° - 90° = 60°, which is the sum of angles ∠BOC and ∠COD.

Since ∠COD is 30° greater than ∠BOC, we can set up an equation where ∠COD = ∠BOC + 30°. If we let x represent ∠BOC, then ∠COD will be x + 30°. Knowing that x + x + 30° = 60°, we can solve for x by setting up the equation 2x + 30° = 60°, which simplifies to 2x = 30°. Hence, ∠BOC (x) is 15° and therefore ∠COD = 15° + 30° = 45°.