6. If $$ m \angle A $$ is $$ 105^{\circ} $$, construct an angle supplementary to $$ \angle A $$.

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UpStudy AI · Accepted Answer

To construct an angle supplementary to $$ \angle A $$, we need to find the angle that, when added to $$ 105^{\circ} $$, equals $$ 180^{\circ} $$.

1. **Identify the known angle**: 
   - $$ m \angle A = 105^{\circ} $$

2. **Use the definition of supplementary angles**: 
   - Two angles are supplementary if their measures add up to $$ 180^{\circ} $$.

3. **Set up the equation**: 
   - Let $$ x $$ be the measure of the supplementary angle.
   - The equation is: 
   $$
   x + 105^{\circ} = 180^{\circ}
   $$

4. **Solve for $$ x $$**: 
   - Rearranging the equation gives:
   $$
   x = 180^{\circ} - 105^{\circ}
   $$

Now, let's calculate $$ x $$.
Calculate the value by following steps:
- step0: Calculate:
  $$180-105$$
- step1: Subtract the numbers:
  $$75$$
The measure of the angle supplementary to $$ \angle A $$ is $$ 75^{\circ} $$.

Thus, $$ m \angle B = 75^{\circ} $$ is the angle that is supplementary to $$ \angle A $$.
The supplementary angle to $$ \angle A $$ is $$ 75^{\circ} $$.

If is , construct an angle
supplementary to .

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