An exterior angle of a triangle is `105^(@)` and its two interior opposite angles are equal. Each of these equal angles is

Options

A. `37(1)/(2)@`
B. `52(1)/(2)@`
C. `72(1)/(2)@`
D. `75^(@)`

Explanation

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the problem
We are given that an exterior angle of a triangle is \(105^\circ\) and that the two interior opposite angles are equal. We need to find the measure of each of these equal angles.

### Step 2: Set up the equation
Let the measure of each of the two equal interior angles be \(x\). According to the properties of triangles, the exterior angle is equal to the sum of the two opposite interior angles. Therefore, we can write the equation:
\[ x + x = 105^\circ \]
This simplifies to:
\[ 2x = 105^\circ \]

### Step 3: Solve for \(x\)
To find \(x\), we divide both sides of the equation by 2:
\[ x = \frac{105^\circ}{2} \]
Calculating this gives:
\[ x = 52.5^\circ \]

### Step 4: Conclusion
Each of the equal interior angles is \(52.5^\circ\).