Identify the combination of angle measures that could form a triangle.
25°, 65°, and 90°
40°, 55°, and 95°
45°, 65°, and 75°
30°, 75°, and 85°
11 answers
The combination of angle measures that could form a triangle is 45°, 65°, and 75°.
The angles of a triangle measure 2x , 3x , and 4x . Using the Triangle Angle Sum Theorem, find the measure of the smallest angle in this triangle.
The sum of the angles in a triangle is always 180 degrees. So, we can write an equation:
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides by 9:
x = 20
Now, we can substitute x back into the expressions for the angles:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
The smallest angle in this triangle is 40 degrees.
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides by 9:
x = 20
Now, we can substitute x back into the expressions for the angles:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
The smallest angle in this triangle is 40 degrees.
Use the image to answer the question.
An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .
Given that angle A = 103 degrees, angle D = 22 degrees, and the sum of the angles in a triangle is 180 degrees, we can find angle C as follows:
Angle A + Angle B + Angle C = 180 degrees
103 degrees + Angle B + Angle C = 180 degrees
Angle B + Angle C = 77 degrees
Now, in triangle BCD, the sum of the angles is also 180 degrees:
Angle B + Angle D + Angle C = 180 degrees
103 degrees + 22 degrees + Angle C = 180 degrees
125 degrees + Angle C = 180 degrees
Substitute the value of Angle B + Angle C from the previous equation:
77 degrees + Angle C = 180 degrees
Angle C = 180 degrees - 77 degrees
Angle C = 103 degrees
Therefore, the measure of the angle at point C is 103 degrees.
Angle A + Angle B + Angle C = 180 degrees
103 degrees + Angle B + Angle C = 180 degrees
Angle B + Angle C = 77 degrees
Now, in triangle BCD, the sum of the angles is also 180 degrees:
Angle B + Angle D + Angle C = 180 degrees
103 degrees + 22 degrees + Angle C = 180 degrees
125 degrees + Angle C = 180 degrees
Substitute the value of Angle B + Angle C from the previous equation:
77 degrees + Angle C = 180 degrees
Angle C = 180 degrees - 77 degrees
Angle C = 103 degrees
Therefore, the measure of the angle at point C is 103 degrees.
Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)° , (3x+3)° , and (2x−7)°
The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
So, we can write the equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplify by combining like terms:
6x - 24 = 180
6x = 204
x = 34
Now, substitute x back into the expressions for the angles to find the measures of the angles:
- First angle: (x-20) = 34 - 20 = 14 degrees
- Second angle: (3x+3) = 3(34) + 3 = 105 degrees
- Third angle: (2x-7) = 2(34) - 7 = 61 degrees
So, the largest angle in the triangle is the second angle which measures 105 degrees.
So, we can write the equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplify by combining like terms:
6x - 24 = 180
6x = 204
x = 34
Now, substitute x back into the expressions for the angles to find the measures of the angles:
- First angle: (x-20) = 34 - 20 = 14 degrees
- Second angle: (3x+3) = 3(34) + 3 = 105 degrees
- Third angle: (2x-7) = 2(34) - 7 = 61 degrees
So, the largest angle in the triangle is the second angle which measures 105 degrees.
Use the image to answer the question.
A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.
Find the measure of the smallest angle of the triangle.
A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.
Find the measure of the smallest angle of the triangle.
Given that the angles of a triangle sum up to 180 degrees, we can set up the equation:
2x + 96 + x + 12 = 180
Combining like terms:
3x + 108 = 180
Subtracting 108 from both sides:
3x = 72
Dividing by 3:
x = 24
Now, we can substitute x back into the expressions for the angles:
2x = 2(24) = 48 degrees
96 degrees
x + 12 = 24 + 12 = 36 degrees
The smallest angle in the triangle is 36 degrees.
2x + 96 + x + 12 = 180
Combining like terms:
3x + 108 = 180
Subtracting 108 from both sides:
3x = 72
Dividing by 3:
x = 24
Now, we can substitute x back into the expressions for the angles:
2x = 2(24) = 48 degrees
96 degrees
x + 12 = 24 + 12 = 36 degrees
The smallest angle in the triangle is 36 degrees.
Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.
5 mm
1 mm
20 mm
2 mm
5 mm
1 mm
20 mm
2 mm
To determine the possible length of the third side of the triangle, we can use the Triangle Inequality Theorem, which states that 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 two given sides are 10 mm and 7 mm. Let the length of the third side be x mm.
So, according to the Triangle Inequality Theorem:
- The sum of the two given sides (10 mm and 7 mm) must be greater than x mm.
- 10 + 7 > x
- 17 > x
Therefore, the length of the third side must be less than the sum of the other two sides, which is 17 mm.
Among the given choices, the only option that is less than 17 mm is 5 mm. Therefore, the length of the third side is 5 mm.
In this case, the two given sides are 10 mm and 7 mm. Let the length of the third side be x mm.
So, according to the Triangle Inequality Theorem:
- The sum of the two given sides (10 mm and 7 mm) must be greater than x mm.
- 10 + 7 > x
- 17 > x
Therefore, the length of the third side must be less than the sum of the other two sides, which is 17 mm.
Among the given choices, the only option that is less than 17 mm is 5 mm. Therefore, the length of the third side is 5 mm.
1 answer