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.(1 point)k,sd
°
Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:
2x + 3x + 4x = 180
Combining like terms, we get:
9x = 180
Dividing by 9 to solve for x, we get:
x = 20
Now, we can substitute x back into the expressions for the angles to find their measures:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees
Therefore, the smallest angle in the triangle measures 40 degrees.
Triangles Unit Test
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Question
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 in the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the three interior angles of a triangle is always 180 degrees.
Given:
- Angle D = 22 degrees
- Angle B = 103 degrees
We can find the measure of angle C by subtracting the sum of angles B and D from 180 degrees:
Angle C = 180 - (Angle B + Angle D)
Angle C = 180 - (103 + 22)
Angle C = 180 - 125
Angle C = 55 degrees
Therefore, the measure of angle C in the triangle is 55 degrees.