Question 92261: 1.) two angles of a quadrilateral are congruent and each of their measures is 110. what is the measure of each of the remaining angles if they are also congruent?
2.) if each of four interior angles of a convex pentagon has a measure of 105, find the measure of the fifth interior angle.
3.) if the sum of the measures of the interior angles of a regular convex polygon is 2160, find the measure of each interior angles.
4.) what is the total number of diagonals that can be drawn in a covex octagon?
5.) what is the sum of the measures of the interior angles of a convex 11-gon?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1.) two angles of a quadrilateral are congruent and each of their measures is 110. what is the measure of each of the remaining angles if they are also congruent?
The sum of the interior angles is 360;
360-2*110=140
(1/2)140 = 70 degrees for each of the other two angles.
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2.) if each of four interior angles of a convex pentagon has a measure of 105, find the measure of the fifth interior angle.
The sum of the interior angles is (5-2)*180 = 540
Your four interior angles add to 420
That leaves 120 for the remaining angle.
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3.) if the sum of the measures of the interior angles of a regular convex polygon is 2160, find the measure of each interior angles.
Let the number of sides be "n"
(n-2)180 = 2160
n-2=12
n=14 sides ; so 14 interior angles
each one is 2160/14 = 154.29 degrees
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4.) what is the total number of diagonals that can be drawn in a covex octagon?
8 sides, so 8 vertices
8C2= 28
But 8 of those are sides of the octagon
Total diagonls = 20
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5.) what is the sum of the measures of the interior angles of a convex 11-gon?
(11-2)*180 = 1620
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Cheers,
Stan H.
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