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How do you find the measure of each interior angle of a regular polygon that has 135 diagonals?
First find the number of sides of the polygon and let it be x:
Rearrange the diagonal formula: 0.5*(x2-3x) = 135 into a quadratic equation
Which is: x2-3x-270 = 0 and solving the equation gives x positive value of 18
Therefore the polygon has 18 sides
Sum of interior angles: (18-2)*180 = 2880 degrees
Each interior angle: 2880/18 = 160 degrees
What else can I help you with?
What is the total number of diagonals in a regular polygon with an interior angle of 120 degrees?
If it is a regular polygon with each interior angle of 120 degrees then it is an hexagon which will have 0.5((6^2)-3*6) equals 9 diagonals
Are interior angles in a polygon equal in measure?
Only if the polygon is "regular".
Is Each of the interior angles in a polygon are equal in measure.?
Only when it is a regular polygon that all interior angles are of equal measure
What is the size of each interior angle of a regular polygon that has 27 diagonals?
13 1/3 °
What is the name of a regular polygon that has 95 diagonals?
There is no such polygon that has 95 diagonals because a 15 sided polygon has 90 diagonals and a 16 sided polygon has 104 diagonals.
What is the total number of diagonals in a regular polygon with an interior angle of 120 degrees?
If it is a regular polygon with each interior angle of 120 degrees then it is an hexagon which will have 0.5((6^2)-3*6) equals 9 diagonals
A regular polygon has an interior angle measure of 168 What kind of polygon is it?
A regular polygon having an interior angle measure of 168o has 30 sides and is called a triacontagon.
Are interior angles in a polygon equal in measure?
Only if the polygon is "regular".
Is Each of the interior angles in a polygon are equal in measure.?
Only when it is a regular polygon that all interior angles are of equal measure
If the measure of an interior angle of a regular polygon is 140 how many sides does the polygon have?
If the measure of an interior angle of a regular polygon is 140o, the polygon is a nonagon (sometimes called an ennagon) having 9 sides.
What is the size of each interior angle of a regular polygon that has 27 diagonals?
13 1/3 °
What is the measure of each interior angle of a fifteen sided regular polygon?
The measure of each interior angle of a fifteen sided regular polygon, a pendedecagon, is 156o.
Which regular polygon has interior angles that measure about 152.3 degrees each?
A 13 sided regular polygon
What is the measure of each interior angle of a 18 sided regular polygon?
The interior angle of an octdecagon, an 18 sided regular polygon, is 160o.
What regular polygon has 9 diagonals?
A regular octadecagon (an eighteen sided polygon) would have nine diagonals.
What is the measure of one interior angle of a regular polygon with 4 sides?
A regular polygon with 4 sides is a square. The measure of any interior angle of a square is 90 degrees.
What is the name of a regular polygon that has 95 diagonals?
There is no such polygon that has 95 diagonals because a 15 sided polygon has 90 diagonals and a 16 sided polygon has 104 diagonals.
