The measure of that angle which is four times its supplement is :

Question

Accepted Answer

To solve the problem of finding the angle which is four times its supplement, we need to understand the relationship between an angle and its supplement. Two angles are supplementary if their sum is 180°.

Let's denote the angle we are looking for as $ x $. Its supplementary angle would then be $ 180° - x $.

According to the problem, the angle $ x $ is four times its supplement. This can be expressed mathematically as:

$$ x = 4 \times (180° - x) $$

Now, let's solve this equation:

1. Expand the equation:
   $$ x = 720° - 4x $$

2. Add $ 4x $ to both sides to get all terms involving $ x $ on one side:
   $$ x + 4x = 720° $$

3. Combine like terms:
   $$ 5x = 720° $$

4. Divide both sides by 5 to solve for $ x $:
   $$ x = \frac{720°}{5} $$
   $$ x = 144° $$

Thus, the angle that is four times its supplement is 144°, which corresponds to Option 2.

**Explanation of why other options are incorrect:**

1. **Option 1: 36°**
   - If the angle were 36°, its supplement would be $ 180° - 36° = 144° $. However, 36° is not four times 144°; rather, it is the other way around. Therefore, this option is incorrect.

2. **Option 3: 155°**
   - If the angle were 155°, its supplement would be $ 180° - 155° = 25° $. However, 155° is not four times 25°; it is actually more than six times 25°. Therefore, this option is incorrect.

3. **Option 4: 180°**
   - An angle of 180° would have a supplement of 0°, as they would sum to 180°. However, 180° cannot be four times 0°, as any number multiplied by zero is zero. Therefore, this option is incorrect.

In conclusion, the correct answer is Option 2: 144°, as it satisfies the condition of being four times its supplement.