Use the equation 2x + 4x + 6x = 180° to solve the measures of the angles in this triangle.
(2 points)
Responses
30°, 30°, and 120°
30°, 30°, and 120°
15°, 60°, and 105°
15°, 60°, and 105°
30°, 60°, and 90°
30°, 60°, and 90°
15°, 75°, and 90°
30°, 60°, and 90°
Explanation:
2x + 4x + 6x = 180°
12x = 180
x = 15
Therefore, the angles are:
2(15) = 30°
4(15) = 60°
6(15) = 90°
Two sides of a triangle are 10 mm and 7 mm. Using the Triangle Inequality Theorem (see picture above), determine the length of the third side from the choices given.
(1 point)
Responses
3 mm
3 mm
5 mm
5 mm
1 mm
1 mm
2 mm
5 mm
Explanation:
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the sum of the given sides 10 mm and 7 mm is 17 mm, which is greater than the third side. Therefore, the third side can be 5 mm.
Two sides of a triangle are 6 in and 8 in. Using the Triangle Inequality Theorem (see picture above), which amount could be the length of the third side from the choices given?
(1 point)
Responses
10 in.
10 in.
2 in.
2 in.
1 in.
10 in.
Explanation: According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the sum of the given sides 6 in and 8 in is 14 in, which is less than the potential third side of 10 in. Therefore, 10 in satisfies the Triangle Inequality Theorem for this scenario.