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 shown.
(1 point)
°
To find the measure of the third angle of the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as angle C. We know that angle A is 120 degrees and angle B is 34 degrees.
Using the Triangle Angle Sum Theorem, we can set up the equation:
angle A + angle B + angle C = 180 degrees
Substituting the known values, we have:
120 + 34 + angle C = 180
Simplifying the equation, we have:
154 + angle C = 180
To solve for angle C, we can subtract 154 from both sides of the equation:
angle C = 180 - 154
angle C = 26 degrees
Therefore, the measure of the third angle of the triangle 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° .(1 point)
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To find the measure of the third angle of the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as angle C. We know that two angles are 34.6° and 52.8°.
Using the Triangle Angle Sum Theorem, we can set up the equation:
angle A + angle B + angle C = 180 degrees
Substituting the known values, we have:
34.6 + 52.8 + angle C = 180
Simplifying the equation, we have:
87.4 + angle C = 180
To solve for angle C, we can subtract 87.4 from both sides of the equation:
angle C = 180 - 87.4
angle C = 92.6 degrees
Therefore, the measure of the third angle of the triangle is 92.6 degrees.
Use the Triangle Angle Sum Theorem to find the measure of the third angle if the first and second angle measure 63°
and 40°
.(1 point)
°
To find the measure of the third angle of the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as angle C. We know that the first angle is 63° and the second angle is 40°.
Using the Triangle Angle Sum Theorem, we can set up the equation:
angle A + angle B + angle C = 180 degrees
Substituting the known values, we have:
63 + 40 + angle C = 180
Simplifying the equation, we have:
103 + angle C = 180
To solve for angle C, we can subtract 103 from both sides of the equation:
angle C = 180 - 103
angle C = 77 degrees
Therefore, the measure of the third angle of the triangle is 77 degrees.
A triangle has two angles measuring 40° and 65° . Use the Triangle Angle Sum Theorem to find the measure of the third angle.(1 point)
°
To find the measure of the third angle of the triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
Let's denote the measure of the third angle as angle C. We know that two angles measure 40° and 65°.
Using the Triangle Angle Sum Theorem, we can set up the equation:
angle A + angle B + angle C = 180 degrees
Substituting the known values, we have:
40 + 65 + angle C = 180
Simplifying the equation, we have:
105 + angle C = 180
To solve for angle C, we can subtract 105 from both sides of the equation:
angle C = 180 - 105
angle C = 75 degrees
Therefore, the measure of the third angle of the triangle is 75 degrees.
A triangle has angle measures of 75°, 41°, and (3x+19)°. Solve for x.
(1 point)
To solve for x, we can use the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles in a triangle is always 180 degrees.
In this case, we know that the three angles in the triangle are 75°, 41°, and (3x+19)°.
Using the Triangle Angle Sum Theorem, we can set up the equation:
75 + 41 + (3x+19) = 180
Combining the like terms, we have:
135 + 3x + 19 = 180
Simplifying the equation, we have:
3x + 154 = 180
To solve for x, we can subtract 154 from both sides of the equation:
3x = 180 - 154
3x = 26
Dividing both sides of the equation by 3, we have:
x = 26/3
Therefore, x is equal to 8 and 2/3 or 8.67.