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

49°
49 degrees

29°
29 degrees

59°

Answer 1

[AI-generated answer — Bot GPT 3.5]

49°

Answer 2

Use the Triangle Angle Sum Theorem to find the measures of each angle for the triangle shown in the diagram.

(1 point)
Responses

46°, 49°, and 85°
46 degrees , 49 degrees , and 85 degrees

50°, 54°, and 93°
50 degrees , 54 degrees , and 93 degrees

42°, 44°, and 79°
42 degrees , 44 degrees , and 79 degrees

46°, 50°, and 85°

Answer 3

[AI-generated answer — Bot GPT 3.5]

46°, 49°, and 85°

Answer 4

The angles of a triangle measure (x+10)° , (x+20)° , and (x+30)° . Find the measure of the smallest angle.(1 point)

Responses

70°
70 degrees

40°
40 degrees

60°
60 degrees

50°

Answer 5

[AI-generated answer — Bot GPT 3.5]

40°

To find the measure of the smallest angle, you need to set up an equation solving the sum of the angles in a triangle. The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180°.

So, you have:
(x + 10) + (x + 20) + (x + 30) = 180
3x + 60 = 180
3x = 120
x = 40

Now, substitute x back into the smallest angle, which is (x + 10) = (40 + 10) = 50°. The smallest angle is 50°.

Answer 6

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

54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees

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
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Answer 7

[AI-generated answer — Bot GPT 3.5]

We will use the Triangle Angle Sum theorem, which states that the sum of the interior angles of a triangle is always 180 degrees.

Given the angles in terms of x:
a = 4x + 14
b = 5x + 4
c = 6x - 3

Sum of angles:
(4x + 14) + (5x + 4) + (6x - 3) = 180
15x + 15 = 180
15x = 165
x = 11

Now, substitute x back into each angle to find their measures:
a = 4(11) + 14 = 58°
b = 5(11) + 4 = 59°
c = 6(11) - 3 = 63°

Therefore, the angles of the triangle measure 58°, 59°, and 63°. This corresponds to the option: 59°, 58°, and 63°.