Use the image to answer the question.
An illustration shows a triangle with vertices as A B C. Angle A on top is 120 degrees and angle B on the left is 34 degrees. Vertex C is on the right.
Use the Triangle Angle Sum Theorem to find the measure of the third angle of the triangle described.
__°
The Triangle Angle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees.
So, in this case:
120 degrees + 34 degrees + x = 180 degrees
154 degrees + x = 180 degrees
x = 26 degrees
Therefore, the measure of the third angle (angle C) is 26 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the third angle of the triangle if the measure of two angles are 34.6° and 52.8°
__°
Given that the measures of two angles are 34.6° and 52.8°, let's denote the third angle as x.
According to the Triangle Angle Sum Theorem, the sum of the three interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
34.6° + 52.8° + x = 180°
87.4° + x = 180°
x = 180° - 87.4°
x = 92.6°
Therefore, the measure of the third angle of the triangle is 92.6°.
Use the Triangle Angle Sum Theorem to find the measure of the third angle if the first and second angle measure 63° and 40°
__°
Given that the measures of the first and second angle are 63° and 40°, let's denote the measure of the third angle as x.
According to the Triangle Angle Sum Theorem, the sum of the three interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
63° + 40° + x = 180°
103° + x = 180°
x = 180° - 103°
x = 77°
Therefore, the measure of the third angle of the triangle is 77°.
A triangle has two angles measuring 40° and 65° . Use the Triangle Angle Sum Theorem to find the measure of the third angle.
__°
Given that the measures of two angles are 40° and 65°, let the measure of the third angle be x.
By the Triangle Angle Sum Theorem, the sum of the three interior angles of a triangle is always 180 degrees. Thus, we have:
40° + 65° + x = 180°
105° + x = 180°
x = 180° - 105°
x = 75°
Therefore, the measure of the third angle of the triangle is 75°.
A triangle has angle measures of 75°, 41°, and (3x+19)°. Solve for x.
__
To find the value of x, we can use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180 degrees. In this case, we have the three angles given:
75° + 41° + (3x + 19)° = 180°
116° + 3x + 19 = 180
3x + 135 = 180
3x = 45
x = 15
Therefore, x = 15.
Use the Triangle Angle Sum Theorem to find the third angle of a triangle if the other two angles measure 25° and 68° .
88°
87°
86°
77°