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
42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees
46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees
46°, 50°, and 85°
46 degrees , 50 degrees , and 85 degrees
50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees
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To find the measures of each angle in the triangle, we use the Triangle Angle Sum Theorem which states that the sum of the angles in a triangle is 180 degrees.
Therefore, we can set up the equation:
(5x - 1) + (8x + 5) + (4x + 6) = 180
17x + 10 = 180
17x = 170
x = 10
Now we can plug in x = 10 to find the measures of each angle:
5x - 1 = 5(10) - 1 = 49°
8x + 5 = 8(10) + 5 = 85°
4x + 6 = 4(10) + 6 = 46°
Therefore, the measures of each angle in the triangle are 49°, 85°, and 46°. So the correct answer is:
46°, 49°, and 85°
The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)
Responses
60°
60 degrees
70°
70 degrees
40°
40 degrees
50°
To find the measure of the smallest angle, we need to determine which expression (x+10), (x+20), or (x+30) represents the smallest value.
Given that the angles of a triangle must add up to 180 degrees, we can set up the following equation:
(x + 10) + (x + 20) + (x + 30) = 180
3x + 60 = 180
3x = 120
x = 40
Now we can find the measures of each angle:
(x + 10) = 40 + 10 = 50°
(x + 20) = 40 + 20 = 60°
(x + 30) = 40 + 30 = 70°
Therefore, the smallest angle is 50°. The correct response is:
50°
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°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
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To find the measures of the angles in the triangle using the Triangle Angle Sum Theorem, we need to add the angles together and set the sum equal to 180 degrees.
Given that the angles in the triangle are:
Angle a = 4x + 14
Angle b = 5x + 4
Angle c = 6x - 3
We can set up the equation:
(4x + 14) + (5x + 4) + (6x - 3) = 180
15x + 15 = 180
15x = 165
x = 11
Now we find the measures of each angle:
Angle a = 4(11) + 14 = 58°
Angle b = 5(11) + 4 = 59°
Angle c = 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°