5Use the Triangle Angle Sum Theorem to find the third angle of a triangle if the other two angles measure 25° and 68° . (1 point)
Responses
77°
77 degrees
88°
88 degrees
86°
86 degrees
87°
The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees.
Given that two angles measure 25° and 68°, we can find the third angle by subtracting the sum of these two angles from 180 degrees:
180° - (25° + 68°) = 87°
Therefore, the third angle measures 87 degrees.
Triangle Angle Sum Theorem Quick Check
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Question
Use the image to answer the question.
An illustration shows a triangle with vertices as D G O. Angle G at the bottom left is right angled. Angle O at the bottom right is 41 degrees. The line D O forms the hypotenuse.
Find the measure of the angle on point D .
(1 point)
Responses
39°
39 degrees
29°
29 degrees
59°
59 degrees
49°
49 degrees
Since the angle at point G is a right angle, it measures 90 degrees. The angle at point O is given as 41 degrees.
To find the measure of the angle at point D, we can use the Triangle Angle Sum Theorem:
Angle D + Angle G + Angle O = 180 degrees
Substituting the known values:
Angle D + 90 degrees + 41 degrees = 180 degrees
Angle D + 131 degrees = 180 degrees
Subtracting 131 degrees from both sides:
Angle D = 180 degrees - 131 degrees
Angle D = 49 degrees
Therefore, the measure of the angle at point D is 49 degrees.
3
I apologize for the confusion. The correct answer to the question is 49°.
Triangle Angle Sum Theorem Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A triangle is shown with its angles measuring left parenthesis 5 x minus 1 right parenthesis degrees, left parenthesis 8 x plus 5 right parenthesis degrees, and left parenthesis 4 x plus 6 right parenthesis degrees.
Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.
(1 point)
Responses
46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
50°, 54°, and 93°
To find the measures of each angle in the triangle, we can set up the equation using the Triangle Angle Sum Theorem:
(5x - 1) + (8x + 5) + (4x + 6) = 180
Simplifying the equation:
17x + 10 = 180
Subtracting 10 from both sides:
17x = 170
Dividing both sides by 17:
x = 10
Now that we have the value of x, we can substitute it back into the expressions for each angle to find their measures:
Angle 1: 5x - 1 = (5 * 10) - 1 = 49°
Angle 2: 8x + 5 = (8 * 10) + 5 = 85°
Angle 3: 4x + 6 = (4 * 10) + 6 = 46°
Therefore, the measures of the angles in the triangle are 49°, 85°, and 46°. The correct response is: 46°, 50°, and 85°.
Triangle Angle Sum Theorem Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
A triangle a b c is shown with angle a measuring 4 x plus 14, angle b measuring 5 x plus 4, and angle c measuring 6 x minus 3.
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
(1 point)
Responses
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
To find the measures of each angle in the triangle, we can set up the equation using the Triangle Angle Sum Theorem:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Simplifying the equation:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now that we have the value of x, we can substitute it back into the expressions for each angle to find their measures:
Angle a: 4x + 14 = (4 * 11) + 14 = 58°
Angle b: 5x + 4 = (5 * 11) + 4 = 59°
Angle c: 6x - 3 = (6 * 11) - 3 = 63°
Therefore, the measures of the angles in the triangle are 58°, 59°, and 63°. The correct response is: 59°, 58°, and 63°.