Question
Find the sum of the measures of the angles of a decagon.
A.
2160°
B.
1800°
C.
1440°
D.
900°
Answers
GPT 3.5
B. 1800°
The sum of the measures of the angles in a decagon is equal to (n-2) * 180, where n is the number of sides in the polygon. In this case, n = 10.
(10-2) * 180 = 8 * 180 = 1440°
The sum of the measures of the angles in a decagon is equal to (n-2) * 180, where n is the number of sides in the polygon. In this case, n = 10.
(10-2) * 180 = 8 * 180 = 1440°
Use the Polygon Angle-Sum Theorem to find the measure of an unknown angle in a polygon.
The Polygon Angle-Sum Theorem
The sum of the measures of the angles of an n-gon is (n−2)180.
Giant Panda 1
What is the measure of ∠D in ABCD?
A.
90°
B.
93°
C.
95°
D.
105°
The Polygon Angle-Sum Theorem
The sum of the measures of the angles of an n-gon is (n−2)180.
Giant Panda 1
What is the measure of ∠D in ABCD?
A.
90°
B.
93°
C.
95°
D.
105°
GPT 3.5
To find the measure of angle ∠D in triangle ABCD, we need to first determine how many sides the polygon has. Since this is a quadrilateral (4 sides), we can use the Polygon Angle-Sum Theorem formula:
Sum of Interior Angles = (n-2) * 180, where n is the number of sides in the polygon.
For a quadrilateral (n=4):
Sum of Interior Angles = (4-2) * 180 = 2 * 180 = 360 degrees
Now, we know that the sum of the interior angles of the quadrilateral ABCD is 360 degrees. Given that the other three angles A, B, and C are labeled as 85°, 80°, and 92° respectively, we can find ∠D:
Sum of Angles A, B, C, and D = 360 degrees
85° + 80° + 92° + ∠D = 360 degrees
(85° + 80° + 92°) + ∠D = 360 degrees
257° + ∠D = 360 degrees
∠D = 360 degrees - 257 degrees
∠D = 103 degrees
Therefore, the measure of angle ∠D in quadrilateral ABCD is 103°.
The closest option provided is D, 105°.
Sum of Interior Angles = (n-2) * 180, where n is the number of sides in the polygon.
For a quadrilateral (n=4):
Sum of Interior Angles = (4-2) * 180 = 2 * 180 = 360 degrees
Now, we know that the sum of the interior angles of the quadrilateral ABCD is 360 degrees. Given that the other three angles A, B, and C are labeled as 85°, 80°, and 92° respectively, we can find ∠D:
Sum of Angles A, B, C, and D = 360 degrees
85° + 80° + 92° + ∠D = 360 degrees
(85° + 80° + 92°) + ∠D = 360 degrees
257° + ∠D = 360 degrees
∠D = 360 degrees - 257 degrees
∠D = 103 degrees
Therefore, the measure of angle ∠D in quadrilateral ABCD is 103°.
The closest option provided is D, 105°.