A regular polygon is partially obscured by a box. What is the sum of t...
Steps 1 & 2: Understand Question and Draw Inferences
To find the sum of the angles of the polygon, you need to know the number of angles.
Knowing that the polygon is regular, the two visible angles (and all the other hidden angles) are equal. You also know that the visible trapezoid has an angle total of 360°
Step 3: Analyze Statement 1
x°= y°
Knowing x equals y doesn’t tell you anything about the angles of the regular polygon.
Statement (1) is not sufficient.
Step 4: Analyze Statement 2
x°+ y°= 72°
The part of the regular polygon that is visible forms a quadrilateral.
This quadrilateral has 4 angles: x°, y° and two interior angles of the regular polygon.
Let each interior angle of the regular polygon = i°
Since the sum of all angles of a quadrilateral is 360°, we can write:
x° + y° + 2i° = 360°
Inserting the information given in Statement 2 in this equation, we get:
72° + 2i° = 360°
Or, 2i° = 288°
i° = 144°
Thus, we now know that every interior angle of the regular polygon measures 144°
Let the regular polygon have n sides.
Then 144°*n = (n -2)*180°
⇒ n = 10.
Therefore, sum of angles of the regular polygon = (n-2)180° = 8*180° = 1,440°.
Statement (2) is sufficient.
Step 5: Analyze Both Statements Together (if needed)
You get a unique answer in step 4, so this step is not required
Answer: Option (B)