OA and OB are opposite rays and a ray OC is inclined. If one of the angles is `75^(@)` , the measurement of the other angle is

Options

A. `105^(@)`
B. `70^(@)`
C. `15^(@)`
D. None of these

Answer

To solve the problem, we need to find the measurement of the angle COA given that angle COB is 75 degrees. Here’s a step-by-step solution:

### Step 1: Understand the Geometry
- We have two opposite rays OA and OB, which means they form a straight line.
- Ray OC is inclined to these rays, creating two angles: angle COA and angle COB.

**Hint:** Remember that opposite rays create a straight angle of 180 degrees.

### Step 2: Set Up the Equation
- Since OA and OB are opposite rays, the sum of angles COA and COB must equal 180 degrees.
- We can express this relationship as:
\[ \text{angle COA} + \text{angle COB} = 180^\circ \]

**Hint:** Use the property of linear pairs to set up your equation.

### Step 3: Substitute the Known Value
- We know that angle COB = 75 degrees. Substitute this value into the equation:
\[ \text{angle COA} + 75^\circ = 180^\circ \]

**Hint:** Make sure to replace the variable with the given angle measurement.

### Step 4: Solve for angle COA
- To find angle COA, we can rearrange the equation:
\[ \text{angle COA} = 180^\circ - 75^\circ \]
- Now perform the subtraction:
\[ \text{angle COA} = 105^\circ \]

**Hint:** Remember to perform the arithmetic carefully to avoid mistakes.

### Step 5: Conclusion
- The measurement of angle COA is 105 degrees.

**Final Answer:** The measurement of the other angle (angle COA) is \( 105^\circ \).

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