Apply the Triangle Inequality Theorem to determine if sides with lengths of 3 feet, 4 feet, and 5 feet form a triangle.(1 point)

Question

Responses

Yes, because the sum of any two sides is less than the third side.
Yes, because the sum of any two sides is less than the third side.

No, because the sum of any two sides is less than the third side.
No, because the sum of any two sides is less than the third side.

No, because two out of three conditions are met.
No, because two out of three conditions are met.

Yes, because the sum of any two sides is greater than the third side.

Answer 1

To determine if the sides with lengths of 3 feet, 4 feet, and 5 feet can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be met:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's check these conditions for the sides of lengths 3 feet, 4 feet, and 5 feet:

1. \(3 + 4 > 5\) → \(7 > 5\) (True)
2. \(3 + 5 > 4\) → \(8 > 4\) (True)
3. \(4 + 5 > 3\) → \(9 > 3\) (True)

Since all three conditions are satisfied, the answer is:

Yes, because the sum of any two sides is greater than the third side.

Answer 2

If a right triangle has an angle that is 65°
, what is the third angle in the triangle?(1 point)
°

Answer 3

In a triangle, the sum of all three angles is always 180 degrees. In a right triangle, one angle is 90 degrees.

Given that one angle in the triangle is 65 degrees, we can find the third angle using the following calculation:

\[ \text{Third angle} = 180^\circ - 90^\circ - 65^\circ \]

Calculating this:

\[ \text{Third angle} = 180^\circ - 90^\circ - 65^\circ = 25^\circ \]

Therefore, the third angle in the triangle is 25 degrees.

Answer 4

What is the measure of the exterior angle x
? (1 point)
37 degrees and 42 degrees
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Answer 5

To find the measure of an exterior angle \( x \) of a triangle, we can use the property that the exterior angle is equal to the sum of the two opposite interior angles.

If the two interior angles are 37 degrees and 42 degrees, we can calculate the exterior angle as follows:

\[ x = 37^\circ + 42^\circ \]

Calculating this:

\[ x = 79^\circ \]

Therefore, the measure of the exterior angle \( x \) is 79 degrees.

Answer 6

also the top is 37 and bottom is 42

Answer 7

If you're referring to a triangle where the angles at the top and bottom are 37 degrees and 42 degrees respectively, then we can find the exterior angle \( x \) by first determining the measure of the third interior angle.

Given:

• Angle 1 (top) = 37 degrees
• Angle 2 (bottom) = 42 degrees

First, let's find the third angle (interior angle) of the triangle using the property that the sum of the angles in a triangle is 180 degrees:

\[ \text{Third angle} = 180^\circ - 37^\circ - 42^\circ \]

Calculating this:

\[ \text{Third angle} = 180^\circ - 79^\circ = 101^\circ \]

Now, the exterior angle \( x \) at the vertex of either the 37-degree angle or the 42-degree angle can be determined. The exterior angle at any vertex is equal to the sum of the opposite interior angles.

For example, to find the exterior angle at the vertex with the 37-degree angle:

\[ x = 42^\circ + 101^\circ \]

Calculating this gives:

\[ x = 143^\circ \]

Alternatively, to find the exterior angle at the vertex with the 42-degree angle:

\[ x = 37^\circ + 101^\circ \]

Calculating this gives:

\[ x = 138^\circ \]

Thus:

1. The exterior angle corresponding to the 37-degree angle is 143 degrees.
2. The exterior angle corresponding to the 42-degree angle is 138 degrees.

If you need a specific exterior angle based on additional context, please clarify!