Question
Find the angle marked x in each of these polygons. x=square ^circ [4] x=square ^circ [4]
Answer
4.7
(150 Votes)
Isabel
Master · Tutor for 5 years
Answer
Since specific polygons and their angles were not provided, here are the hypothetical answers based on the examples:- For the quadrilateral:
.- For the pentagon:
.Please provide the specific details for each polygon to get the exact answers for the question as stated.
Explanation
## Step 1: Understand the formula for the sum of interior angles of a polygon.### The formula is: \( \mathbf{(n - 2) \times 180^\circ} \), where
is the number of sides in the polygon.## Step 2: For each polygon, count the number of sides (or use the given number of sides) to calculate the total sum of the interior angles using the formula from Step 1.## Step 3: Add up the known angles provided in the problem.## Step 4: Subtract the sum of the known angles from the total sum of the interior angles to find the value of the missing angle
.## Step 5: Apply the steps above to each polygon separately to find each missing angle.Given the lack of specific details for the polygons in the question, I will illustrate with a hypothetical example for a quadrilateral (4 sides) and a pentagon (5 sides).### Example for a quadrilateral:- Suppose the known angles are 90°, 80°, and 100°.- Total sum of interior angles = \( (4 - 2) \times 180^\circ = 360^\circ \).- Sum of known angles =
.- Missing angle
.### Example for a pentagon:- Suppose the known angles are 108°, 102°, 120°, and 90°.- Total sum of interior angles = \( (5 - 2) \times 180^\circ = 540^\circ \).- Sum of known angles =
.- Missing angle
.