use the dropdowns to complete the explanation of the triangle angle sum theorem
the blank of all blank angles in a triangle is blank degrees
11 answers
The sum of all interior angles in a triangle is always 180 degrees.
is it the sum of 2 3 4
No, it is not the sum of 2, 3, or 4 angles. The sum of all interior angles in a triangle is always 180 degrees.
two angles in a triangle measure 34 and 101. what is the measure of the third angle?
32
39
45
54
32
39
45
54
To find the measure of the third angle in a triangle, we can use the triangle angle sum theorem, which states that the sum of all interior angles in a triangle is always 180 degrees.
Let the measure of the third angle be x.
We know that the sum of the measures of the three angles is 180 degrees:
34 + 101 + x = 180
Simplifying the equation:
135 + x = 180
Subtracting 135 from both sides of the equation:
x = 180 - 135
x = 45
Therefore, the measure of the third angle is 45 degrees.
Let the measure of the third angle be x.
We know that the sum of the measures of the three angles is 180 degrees:
34 + 101 + x = 180
Simplifying the equation:
135 + x = 180
Subtracting 135 from both sides of the equation:
x = 180 - 135
x = 45
Therefore, the measure of the third angle is 45 degrees.
identify the combination of angle measures that could form a triangle.
30 75 85
25 65 75
45 65 75
40 55 95
30 75 85
25 65 75
45 65 75
40 55 95
The combination of angle measures that could form a triangle is:
45, 65, 75
To determine if a combination of angle measures can form a triangle, we need to ensure that the sum of any two angles is greater than the measure of the third angle. Let's check each combination:
1) 30, 75, 85:
30 + 75 = 105, which is greater than 85.
75 + 85 = 160, which is also greater than 30.
However, 30 + 85 = 115, which is NOT greater than 75.
Therefore, 30, 75, 85 cannot form a triangle.
2) 25, 65, 75:
25 + 65 = 90, which is greater than 75.
65 + 75 = 140, which is also greater than 25.
However, 25 + 75 = 100, which is NOT greater than 65.
Therefore, 25, 65, 75 cannot form a triangle.
3) 45, 65, 75:
45 + 65 = 110, which is greater than 75.
65 + 75 = 140, which is also greater than 45.
45 + 75 = 120, which is greater than 65.
Therefore, 45, 65, 75 can form a triangle.
4) 40, 55, 95:
40 + 55 = 95, which is NOT greater than 95 itself.
Therefore, 40, 55, 95 cannot form a triangle.
In conclusion, the combination of angle measures that could form a triangle is 45, 65, 75.
45, 65, 75
To determine if a combination of angle measures can form a triangle, we need to ensure that the sum of any two angles is greater than the measure of the third angle. Let's check each combination:
1) 30, 75, 85:
30 + 75 = 105, which is greater than 85.
75 + 85 = 160, which is also greater than 30.
However, 30 + 85 = 115, which is NOT greater than 75.
Therefore, 30, 75, 85 cannot form a triangle.
2) 25, 65, 75:
25 + 65 = 90, which is greater than 75.
65 + 75 = 140, which is also greater than 25.
However, 25 + 75 = 100, which is NOT greater than 65.
Therefore, 25, 65, 75 cannot form a triangle.
3) 45, 65, 75:
45 + 65 = 110, which is greater than 75.
65 + 75 = 140, which is also greater than 45.
45 + 75 = 120, which is greater than 65.
Therefore, 45, 65, 75 can form a triangle.
4) 40, 55, 95:
40 + 55 = 95, which is NOT greater than 95 itself.
Therefore, 40, 55, 95 cannot form a triangle.
In conclusion, the combination of angle measures that could form a triangle is 45, 65, 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
According to the triangle angle sum theorem, the sum of all three interior angles in a triangle is always 180 degrees.
Let's denote the measure of the smallest angle as 2x. The measure of the other two angles are 3x and 4x.
Therefore, we can set up the equation:
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides of the equation by 9:
x = 20
Now, we can find the measure of the smallest angle by substituting x back into the expression 2x:
2(20) = 40
Thus, the measure of the smallest angle in this triangle is 40 degrees.
Let's denote the measure of the smallest angle as 2x. The measure of the other two angles are 3x and 4x.
Therefore, we can set up the equation:
2x + 3x + 4x = 180
Combining like terms:
9x = 180
Dividing both sides of the equation by 9:
x = 20
Now, we can find the measure of the smallest angle by substituting x back into the expression 2x:
2(20) = 40
Thus, the measure of the smallest angle in this triangle is 40 degrees.
a image show abcd the a and b are 103 degrees and d is 22 use the triangle sum theorem to find the measure of the angle on point C
To find the measure of the angle at point C, we can use the triangle angle sum theorem, which states that the sum of all interior angles in a triangle is always 180 degrees.
From the given information, we know that angle A is 103 degrees, angle B is 103 degrees, and angle D is 22 degrees.
Let the measure of the angle at point C be x.
Now, we can set up the equation:
Angle A + Angle B + Angle C + Angle D = 180
Substituting the given angle measures:
103 + 103 + x + 22 = 180
Simplifying the equation:
206 + x + 22 = 180
Combining like terms:
x + 228 = 180
Subtracting 228 from both sides of the equation:
x = 180 - 228
x = -48
Therefore, the measure of the angle at point C is -48 degrees. However, it is not possible for an angle to have a negative measure. Hence, the given angle measures do not form a valid triangle.
From the given information, we know that angle A is 103 degrees, angle B is 103 degrees, and angle D is 22 degrees.
Let the measure of the angle at point C be x.
Now, we can set up the equation:
Angle A + Angle B + Angle C + Angle D = 180
Substituting the given angle measures:
103 + 103 + x + 22 = 180
Simplifying the equation:
206 + x + 22 = 180
Combining like terms:
x + 228 = 180
Subtracting 228 from both sides of the equation:
x = 180 - 228
x = -48
Therefore, the measure of the angle at point C is -48 degrees. However, it is not possible for an angle to have a negative measure. Hence, the given angle measures do not form a valid triangle.