QuestionWhich set of angles can form a triangle? A) $20^{\circ}, 45^{\circ}, 120^{\circ}$ B) $100^{\circ}, 130^{\circ}, 130^{\circ}$ C) $35^{\circ}, 60^{\circ}, 85^{\circ}$ D) $25^{\circ}, 55^{\circ}, 110^{\circ}$

Studdy Solution

STEP 1

Assumptions1. A triangle has three angles. . The sum of the measures of the angles in a triangle is always $180^{\circ}$ .

STEP 2

We will check each option to see if the sum of the angle measures is $180^{\circ}$ .
For option A, we add the given angle measures.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ}$

STEP 3

Calculate the sum of the angles for option A.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ} =185^{\circ}$

STEP 4

Since the sum of the angles in option A is not equal to $180^{\circ}$ , option A cannot be the angle measures of a triangle.
Next, for option B, we add the given angle measures.
$Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ}$

STEP 5

Calculate the sum of the angles for option B.
$Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ} =360^{\circ}$

STEP 6

Since the sum of the angles in option B is not equal to $180^{\circ}$ , option B cannot be the angle measures of a triangle.
Next, for option C, we add the given angle measures.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ}$

STEP 7

Calculate the sum of the angles for option C.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ} =180^{\circ}$

STEP 8

Since the sum of the angles in option C is equal to $180^{\circ}$ , option C could be the angle measures of a triangle.
Finally, for option D, we add the given angle measures.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ}$

STEP 9

Calculate the sum of the angles for option D.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ} =190^{\circ}$

STEP 10

Since the sum of the angles in option D is not equal to $180^{\circ}$ , option D cannot be the angle measures of a triangle.
The only option that could be the angle measures of a triangle is option C $35^{\circ},60^{\circ},85^{\circ}$ .

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QuestionWhich set of angles can form a triangle? A) $20^{\circ}, 45^{\circ}, 120^{\circ}$ B) $100^{\circ}, 130^{\circ}, 130^{\circ}$ C) $35^{\circ}, 60^{\circ}, 85^{\circ}$ D) $25^{\circ}, 55^{\circ}, 110^{\circ}$

Studdy Solution

STEP 1

Assumptions1. A triangle has three angles. . The sum of the measures of the angles in a triangle is always $180^{\circ}$ .

STEP 2

We will check each option to see if the sum of the angle measures is $180^{\circ}$ .
For option A, we add the given angle measures.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ}$

STEP 3

Calculate the sum of the angles for option A.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ} =185^{\circ}$

STEP 4

Since the sum of the angles in option A is not equal to $180^{\circ}$ , option A cannot be the angle measures of a triangle.
Next, for option B, we add the given angle measures.
$Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ}$

STEP 5

Calculate the sum of the angles for option B.
$Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ} =360^{\circ}$

STEP 6

Since the sum of the angles in option B is not equal to $180^{\circ}$ , option B cannot be the angle measures of a triangle.
Next, for option C, we add the given angle measures.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ}$

STEP 7

Calculate the sum of the angles for option C.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ} =180^{\circ}$

STEP 8

Since the sum of the angles in option C is equal to $180^{\circ}$ , option C could be the angle measures of a triangle.
Finally, for option D, we add the given angle measures.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ}$

STEP 9

Calculate the sum of the angles for option D.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ} =190^{\circ}$

STEP 10

Since the sum of the angles in option D is not equal to $180^{\circ}$ , option D cannot be the angle measures of a triangle.
The only option that could be the angle measures of a triangle is option C $35^{\circ},60^{\circ},85^{\circ}$ .

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Studdy Solution

STEP 1

Assumptions1. A triangle has three angles. . The sum of the measures of the angles in a triangle is always 180∘180^{\circ}180∘.

STEP 2

We will check each option to see if the sum of the angle measures is 180∘180^{\circ}180∘.For option A, we add the given angle measures.Sum of angles=20∘+45∘+120∘Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ}Sumofangles=20∘+45∘+120∘

STEP 3

Calculate the sum of the angles for option A.Sum of angles=20∘+45∘+120∘=185∘Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ} =185^{\circ}Sumofangles=20∘+45∘+120∘=185∘

STEP 4

STEP 5

Calculate the sum of the angles for option B.Sum of angles=100∘+130∘+130∘=360∘Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ} =360^{\circ}Sumofangles=100∘+130∘+130∘=360∘

STEP 6

Since the sum of the angles in option B is not equal to 180∘180^{\circ}180∘, option B cannot be the angle measures of a triangle.Next, for option C, we add the given angle measures.Sum of angles=35∘+60∘+85∘Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ}Sumofangles=35∘+60∘+85∘

STEP 7

Calculate the sum of the angles for option C.Sum of angles=35∘+60∘+85∘=180∘Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ} =180^{\circ}Sumofangles=35∘+60∘+85∘=180∘

STEP 8

Since the sum of the angles in option C is equal to 180∘180^{\circ}180∘, option C could be the angle measures of a triangle.Finally, for option D, we add the given angle measures.Sum of angles=25∘+55∘+110∘Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ}Sumofangles=25∘+55∘+110∘

STEP 9

Calculate the sum of the angles for option D.Sum of angles=25∘+55∘+110∘=190∘Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ} =190^{\circ}Sumofangles=25∘+55∘+110∘=190∘

STEP 10

Since the sum of the angles in option D is not equal to 180∘180^{\circ}180∘, option D cannot be the angle measures of a triangle.The only option that could be the angle measures of a triangle is option C 35∘,60∘,85∘35^{\circ},60^{\circ},85^{\circ}35∘,60∘,85∘.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. A triangle has three angles. . The sum of the measures of the angles in a triangle is always $180^{\circ}$ .

We will check each option to see if the sum of the angle measures is $180^{\circ}$ .
For option A, we add the given angle measures.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ}$

Calculate the sum of the angles for option A.
$Sum\, of\, angles =20^{\circ} +45^{\circ} +120^{\circ} =185^{\circ}$

Calculate the sum of the angles for option B.
$Sum\, of\, angles =100^{\circ} +130^{\circ} +130^{\circ} =360^{\circ}$

Since the sum of the angles in option B is not equal to $180^{\circ}$ , option B cannot be the angle measures of a triangle.
Next, for option C, we add the given angle measures.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ}$

Calculate the sum of the angles for option C.
$Sum\, of\, angles =35^{\circ} +60^{\circ} +85^{\circ} =180^{\circ}$

Since the sum of the angles in option C is equal to $180^{\circ}$ , option C could be the angle measures of a triangle.
Finally, for option D, we add the given angle measures.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ}$

Calculate the sum of the angles for option D.
$Sum\, of\, angles =25^{\circ} +55^{\circ} +110^{\circ} =190^{\circ}$

Since the sum of the angles in option D is not equal to $180^{\circ}$ , option D cannot be the angle measures of a triangle.
The only option that could be the angle measures of a triangle is option C $35^{\circ},60^{\circ},85^{\circ}$ .