Use the image to answer the question.

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.

39°
49°
59°
29°

Answer 1

Let x be the measure of the angle at D. Since the sum of the angles in a triangle is 180 degrees, we have:

x + 90 + 41 = 180
x + 131 = 180
x = 49

Therefore, the measure of the angle at point D is 49 degrees.

The answer is 49°.

Answer 2

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 described.

a. 50°, 54°, and 93°
b. 46°, 50°, and 85°
c. 42°, 44°, and 79°
d. 46°, 49°, and 85°

Answer 3

The Triangle Angle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees.

The angles are given as:
5x - 1
8x + 5
4x + 6

Setting up the equation:
5x - 1 + 8x + 5 + 4x + 6 = 180
17x + 10 = 180
17x = 170
x = 10

Now, substituting x back into the angle measurements:
Angle 1: 5(10) - 1 = 49 degrees
Angle 2: 8(10) + 5 = 85 degrees
Angle 3: 4(10) + 6 = 46 degrees

Therefore, the measures of each angle in the triangle are 49°, 85°, and 46°.

The answer is d. 46°, 85°, and 49°.

Answer 4

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

70°
50°
40°
60°

Answer 5

The sum of the angles in a triangle is always 180 degrees. Setting up the equation with the given angles:

(x + 10) + (x + 20) + (x + 30) = 180
3x + 60 = 180
3x = 120
x = 40

Now, substituting x back into the angles:
Angle 1: x + 10 = 40 + 10 = 50 degrees
Angle 2: x + 20 = 40 + 20 = 60 degrees
Angle 3: x + 30 = 40 + 30 = 70 degrees

Therefore, the smallest angle measures 50 degrees.

The answer 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.

a. 59°, 63°, and 48°
b. 57°, 54°, and 69°
c. 59°, 58°, and 63°
d. 54°, 44°, and 82°

Answer 7

The Triangle Angle Sum Theorem states that the sum of the three interior angles of a triangle is always 180 degrees.

Given:
Angle a = 4x + 14
Angle b = 5x + 4
Angle c = 6x - 3

Setting up the equation:
(4x + 14) + (5x + 4) + (6x - 3) = 180
15x + 15 = 180
15x = 165
x = 11

Now, substituting x back into the angles:
Angle a: 4(11) + 14 = 58°
Angle b: 5(11) + 4 = 59°
Angle c: 6(11) - 3 = 63°

Therefore, the measures of the angles for the triangle are 58°, 59°, and 63°.

The answer is c. 59°, 58°, and 63°.