is it possible for the interior angles of a regular polygon to each measure 77 degrees?
yes or no
No. For a regular polygon with n sides, the measure of each interior angle is given by:
( n - 2 ) * 180 / n
If we substitute n = 360 / 77, we get a non-integer result, which means that it is not possible for the interior angles of a regular polygon to each measure 77 degrees.
Is this statement #2 is inverse, converse, or contrapostive of statement 1
1-If a polygon is a quadrilateral then it has 4 sides
2-If a polygon does not have 4 sides then it is not a quadrilateral
Statement #2 is the contrapositive of statement #1.
what is the best statement for Alternate interior angles are congruent
<ABD is congruent to <CDB
<A is congruent to <C
<ADB is congruent to <CBD
<ABC is congruent to <ABC
The best statement for alternate interior angles are congruent is:
"If a transversal intersects two parallel lines, then the alternate interior angles are congruent."
based on the answer choices which one fits?
Out of the answer choices provided, the statement that fits the best is:
"When a transversal intersects two parallel lines, the alternate interior angles are congruent."
<ABD is congruent to <CDB
<A is congruent to <C
<ADB is congruent to <CBD
<ABC is congruent to <ABC
out of those choices which one?
Of the answer choices provided, none of them is an accurate statement for the fact that alternate interior angles are congruent.
The statement "Alternate interior angles are congruent" applies specifically to situations where a transversal intersects two parallel lines.
Therefore, the best statement for this fact is: "When a transversal intersects two parallel lines, the alternate interior angles are congruent."
No, it is not possible for the interior angles of a regular polygon to each measure 77 degrees.
To understand why, we need to recall a formula for calculating the measure of an interior angle of a regular polygon. The formula is:
Interior Angle = (n-2) * 180 / n
where "n" represents the number of sides of the polygon. In a regular polygon, all interior angles are equal.
If we substitute the given measure of 77 degrees into this formula, we get:
77 = (n-2) * 180 / n
Cross-multiplying and simplifying, we have:
77n = 180n - 360
360 = 180n - 77n
360 = 103n
n = 360 / 103 ≈ 3.495
Here, n represents the number of sides of the supposed regular polygon. However, we can see that n is not a whole number, which indicates that there is no whole number of sides that can satisfy the equation.
Therefore, it is not possible for the interior angles of a regular polygon to each measure 77 degrees.