Question

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A triangle is shown with its angles measuring 2 x, 96 degrees, and x plus 12 degrees.

Find the measure of the smallest angle of the triangle.

Answer 1

Two sides of a triangle are 10 mm and 7 mm. Determine the length of the third side from the choices given.(1 point)
Responses

1 mm
1 mm

20 mm
20 mm

2 mm
2 mm

5 mm

Answer 2

Complete the condition statements that must be met in order for three side lengths— a , b , and c —to create a triangle.(1 point)
a
b+c and a
b−c

Answer 3

To find the measure of the smallest angle of the triangle, we need to add up all the angles and then find the smallest one.

So we have:
2x + 96 + x + 12 = 180 (sum of angles in a triangle is 180 degrees)

Combining like terms, we get:
3x + 108 = 180

Subtracting 108 from both sides:
3x = 72

Dividing by 3:
x = 24

Now we can find the measure of the smallest angle by substituting x back into the equation for the smallest angle:
2x = 2(24) = 48 degrees

Therefore, the smallest angle of the triangle measures 48 degrees.

Answer 4

To determine the possible lengths of the third side of the triangle, we can use the triangle inequality principle which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. According to the given information, the two sides given are 10 mm and 7 mm.

Thus, we have:

10 + 7 > x
17 > x

Given the options, the only valid choice is 5 mm. Therefore, the length of the third side must be 5 mm in order for it to form a triangle with side lengths 10 mm, 7 mm, and 5 mm.

Answer 5

To determine whether three side lengths a, b, and c can form a triangle, the following conditions must be met:

1. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side:
a + b > c
a + c > b
b + c > a

2. The difference between the lengths of any two sides of a triangle must be less than the length of the third side:
|a - b| < c
|a - c| < b
|b - c| < a

These conditions ensure that the three sides can form a closed triangle with no gaps or overlaps.