Use 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
87°
87 degrees
86°
The third angle can be found by subtracting the sum of the other two angles from 180°.
180° - (25° + 68°) = 180° - 93° = 87°
Therefore, the third angle measures 87°.
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
29°
29 degrees
59°
59 degrees
39°
39 degrees
49°
Since angle O is 41 degrees, angle D measures:
90° (right angle) - 41° = 49°
Therefore, the measure of angle D is 49°.
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
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
42°, 44°, and 79°
The sum of the angles in a triangle is 180 degrees.
Given:
5x - 1 + 8x + 5 + 4x + 6 = 180
Combine like terms:
17x + 10 = 180
17x = 170
x = 10
Now, substitute x back into the expressions for the angles:
5(10) - 1 = 49 degrees
8(10) + 5 = 85 degrees
4(10) + 6 = 46 degrees
Therefore, the measure of each angle is 46°, 85°, and 49°.
The correct response is: 46°, 85°, and 49°
The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)
Responses
40°
40 degrees
60°
60 degrees
70°
70 degrees
50°
50 degrees
To find the smallest angle, we need to identify the expression for the smallest angle and then evaluate it.
Given:
Angles of the triangle measure (x+10)°, (x+20)°, and (x+30)°.
The smallest angle is the one with the smallest coefficient of x, which is (x+10).
To find the smallest angle, we evaluate (x+10) when x = 0 since x is a variable that can vary.
When x = 0:
(x+10) = 0 + 10 = 10
Therefore, the measure of the smallest angle is 10 degrees. So, the correct answer is not among the given options. It should be 10°.
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
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
54°, 44°, and 82°
To find the measures of the angles in the triangle, we can use the Triangle Angle Sum Theorem which states that the sum of the interior angles of a triangle is always 180 degrees.
Given:
Angle a = 4x + 14
Angle b = 5x + 4
Angle c = 6x - 3
Sum of the angles:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Combine like terms:
15x + 15 = 180
15x = 165
x = 11
Now, substitute x back into the expressions for the angles:
Angle a = 4(11) + 14 = 58 + 14 = 72 degrees
Angle b = 5(11) + 4 = 55 + 4 = 59 degrees
Angle c = 6(11) - 3 = 66 - 3 = 63 degrees
Therefore, the measure of the angles in the triangle is 72°, 59°, and 63°.
The correct response is: 72°, 59°, and 63°.