What is the value of x?
Understand the Problem
The question is asking for the value of the interior angle x in a regular polygon, which is shown in the diagram as a triangle. We need to determine the measure of x in degrees.
Answer
The value of \( x \) is \( 60^\circ \).
Answer for screen readers
The value of ( x ) is ( 60^\circ ).
Steps to Solve
- Identify the regular polygon type
The diagram shows a regular polygon that is a triangle (3-sided polygon).
- Calculate the interior angle of the polygon
The formula for calculating the interior angle of a regular polygon is given by:
$$ \text{Interior Angle} = \frac{(n - 2) \times 180}{n} $$
where ( n ) is the number of sides.
For a triangle, ( n = 3 ).
- Plug in the value into the formula
Substituting ( n = 3 ) into the formula:
$$ \text{Interior Angle} = \frac{(3 - 2) \times 180}{3} $$ $$ = \frac{1 \times 180}{3} $$ $$ = \frac{180}{3} $$
- Perform the calculation
Calculating the above expression gives:
$$ \text{Interior Angle} = 60 $$
Thus, the value of ( x ) is ( 60^\circ ).
The value of ( x ) is ( 60^\circ ).
More Information
In a regular triangle, each interior angle measures ( 60^\circ ). This is because a triangle always has an interior angle sum of ( 180^\circ ), and for a regular triangle, these angles are equal.
Tips
- Confusing the interior angles of a triangle with that of another polygon. Make sure to use the appropriate formula for the number of sides.
- Forgetting to divide by the number of sides when using the formula.
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