bro gimme the anwser
I'm sorry, but I cannot provide answers without knowing the specific question you're referring to. Could you please provide more information?
oh sorry
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 .
(1 point)
°
To find the measure of angle C, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
Given:
Angle D = 22 degrees
Angle ABC = 103 degrees
To find angle C, we can start by finding the measure of angle BCD, which is the exterior angle of triangle ABC at vertex C.
The exterior angle of a triangle is equal to the sum of its interior opposite angles, so we can calculate:
Angle BCD = Angle ABC + Angle C = 103 degrees + Angle C
Also, since Angle BCD is an exterior angle, we know that it is equal to the sum of the two remote interior angles at vertices B and D. One of these remote interior angles is Angle ABC, which is 103 degrees, and the other remote interior angle at point D is given as 22 degrees.
Therefore, we have:
Angle BCD = Angle ABC + Angle C = 103 degrees + Angle C
Angle BCD = Angle ABC + Angle D = 103 degrees + 22 degrees
According to the Triangle Angle Sum Theorem, the sum of angles BCD, ABC, and ACD must be equal to 180 degrees.
So we can write the equation:
BCD + ABC + ACD = 180 degrees
Substituting the known values, we have:
(103 degrees + Angle C) + 22 degrees + Angle C = 180 degrees
Simplifying the equation, we get:
125 degrees + 2 * Angle C = 180 degrees
Subtracting 125 degrees from both sides, we obtain:
2 * Angle C = 55 degrees
Dividing both sides by 2, we find:
Angle C = 27.5 degrees
Therefore, the measure of angle C is 27.5 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.(1 point)
°Complete the condition statements that must be met in order for three side lengths—a, b, and c—to create a triangle.(1 point)
a
b+c and a
b−c
To find the measure of the smallest angle of the triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Given:
Angle 1 = 2x
Angle 2 = 96 degrees
Angle 3 = x + 12 degrees
To find the smallest angle, we need to determine the smallest value among Angle 1, Angle 2, and Angle 3.
Since we don't have an exact value for x, we need to consider different cases to find the smallest angle:
1. If Angle 1 (2x) is the smallest angle:
2x < 96 and 2x < x + 12
Simplifying the inequalities:
2x - x < 96 and 2x - x < 12
x < 96 and x < 12
Since both conditions must be met, the smallest possible value for x is 11. Therefore, Angle 1 is smallest when x = 11.
Substituting x = 11 into Angle 1:
Angle 1 = 2x = 2 * 11 = 22 degrees
2. If Angle 2 (96 degrees) is the smallest angle:
96 < 2x and 96 < x + 12
Simplifying the inequalities:
x > 48 and x > 84
Since both conditions must be met, there is no possible value for x that satisfies both inequalities. Therefore, Angle 2 cannot be the smallest angle.
3. If Angle 3 (x + 12) is the smallest angle:
x + 12 < 2x and x + 12 < 96
Simplifying the inequalities:
12 < x and x > 84
Since both conditions must be met, the smallest possible value for x is 85. Therefore, Angle 3 is the smallest when x = 85.
Substituting x = 85 into Angle 3:
Angle 3 = x + 12 = 85 + 12 = 97 degrees
Therefore, the smallest angle of the triangle is 22 degrees.
Now, let's address the condition statements for three side lengths (a, b, and c) to create a triangle:
Condition 1: Triangle Inequality Theorem
In order for three side lengths to create a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Condition 2: Non-Negative Side Lengths
All three side lengths must have non-negative values (greater than or equal to 0).
For the given side lengths to create a triangle, the following condition statements must be met:
a + b > c
a + c > b
b + c > a
Additionally, the side lengths a, b, and c should all be non-negative (a ≥ 0, b ≥ 0, c ≥ 0).