Question

Find the measure of each missing angle:

63°
2°
38°
3°
1°
11°
A) 61°, 58°
B) 56°, 57°
C) 57°, 61°
D) 58°, 56°

Answer 1

The measure of each missing angle is 57°, 61°

The correct option is C.

Step-by-step explanation:

To find the missing angles, we can use the fact that the sum of interior angles in any polygon is given by the formula (n-2) × 180°, where n is the number of sides. For the given set of angles, we can assume that they belong to a polygon and use this formula.

Let's add the given angles:

63° + 2° + 38° + 3° + 1° + 11° = 118°

Now, using the formula for the sum of interior angles, if we assume it's a hexagon (n=6), the sum should be
`\((6-2) * 180° = 720°.\)` The difference between the assumed sum and the calculated sum gives us the missing angles:

`\[720° - 118° = 602°.\]`

Now, we distribute this difference among the missing angles. If we denote the missing angles as
`\(x\) and \(y\),` we get the equations:

`\[x + y = 602°\]`

`\[x + 63° + 2° + 38° + 3° + 1° + 11° = 720°.\]`

Solving these equations, we find
`\(x = 57°\) and \(y = 61°\)`, confirming our choice of answer C.

In summary, by using the formula for the sum of interior angles and solving the equations derived from it, we can determine the missing angles in the given set, leading us to the conclusion that the correct answer is C) 57°, 61°.

The correct option is C.