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, we can use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
We already know that angle D is 22 degrees and angle ABC is 103 degrees. To find angle C, we can subtract the sum of these two angles from 180 degrees:
Angle C = 180 degrees - Angle ABC - Angle D
= 180 degrees - 103 degrees - 22 degrees
Calculating this, we find:
Angle C = 55 degrees
Therefore, the measure of angle C is 55 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)° .
According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is always 180 degrees. Therefore, in this triangle, we have:
(x - 20)° + (3x + 3)° + (2x - 7)° = 180°
Now, we can solve for x:
x - 20 + 3x + 3 + 2x - 7 = 180
6x - 24 = 180
6x = 204
x = 34
Now that we have found the value of x, we can substitute it back into the angle measures to find the largest angle.
The three angles in the triangle are:
(x - 20)° = (34 - 20)° = 14°
(3x + 3)° = (3(34) + 3)° = 105°
(2x - 7)° = (2(34) - 7)° = 61°
Comparing the three angles, we see that the largest angle is 105°.
Therefore, the largest angle in the triangle is 105 degrees.