Identify the combination of angle measures that could form a triangle

Question

25, 65, and 90

40, 55, and 95

30,75, and 85

45, 65 and 75

Answer 1

The only combination of angle measures that could form a triangle is 30, 75, and 85. This is because the sum of the interior angles of a triangle must always equal 180 degrees.

Answer 2

The angle of a triangle measure 2x, 3x and 4x. Using the triangle angle sum theorem, find the measure of the smallest angle in this triangle

Answer 3

The sum of the interior angles of a triangle is always 180 degrees.

So, in this case, we can write the equation:
2x + 3x + 4x = 180
9x = 180
x = 20

Now, we can find the measure of each angle:
2x = 2(20) = 40 degrees
3x = 3(20) = 60 degrees
4x = 4(20) = 80 degrees

Therefore, the smallest angle in this triangle measures 40 degrees.

Answer 4

Use the triangle angle sum theorem to find the largest angle in a triangle with angle measurements of (x - 20), (3x + 3) and (2x - 7)

Answer 5

The sum of the interior angles of a triangle is always 180 degrees.

So, in this case, we can write the equation:
(x - 20) + (3x + 3) + (2x - 7) = 180
6x - 24 = 180
6x = 204
x = 34

Now, we can find the measure of each angle:
(x - 20) = 34 - 20 = 14 degrees
(3x + 3) = 3(34) + 3 = 105 degrees
(2x - 7) = 2(34) - 7 = 61 degrees

Therefore, the largest angle in this triangle measures 105 degrees.

Answer 6

Find the measure of the smallest angle of the triangle 96, 2x and (x + 12)

Answer 7

To determine the smallest angle in the triangle, we need to find the smallest angle measurement among 96, 2x, and (x + 12) where x is a variable.

Let's set up the inequalities to see which angle measure is the smallest:

96 < 2x
x + 12 < 96

From the first inequality, we can solve for x:
2x > 96
x > 48

From the second inequality, we can solve for x:
x < 84

Combining the two results, we get:
48 < x < 84

Now, we need to test the possible values of x within this range to find the smallest angle measurement.

Let's try x = 50:
The angles would be 96, 100, and 62. The smallest angle would be 62.

Therefore, the measure of the smallest angle in this triangle is 62 degrees.

Answer 8

Two sides of a triangle are 10mm and 7mm. Determine the length of the third side from the choices given

Answer 9

To determine the possible length of the third side of the triangle, we can use the Triangle Inequality Theorem, 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.

In this case, let's denote the third side by x. We can set up an inequality:
- 10 + 7 < x < 10 + 7

This simplifies to:
- 3 < x < 17

Therefore, the length of the third side must be greater than 3mm but less than 17mm.

From the choices given:
- 5mm
- 6mm
- 12mm
- 15mm

The only valid option within the range is 12mm.

Therefore, the length of the third side of the triangle is 12mm.

Answer 10

Sorry the options are

1mm
5mm
20mm
2mm

Answer 11

Given that two sides of a triangle are 10mm and 7mm, the third side can be any length that satisfies the Triangle Inequality Theorem, 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's denote the length of the third side as x. According to the theorem, the third side must satisfy the following inequality:
|10 - 7| < x < 10 + 7.

This simplifies to:
3 < x < 17.

Based on the options provided:
- 1mm does not fall within the valid range of 3 < x < 17.
- 5mm falls within the valid range of 3 < 5 < 17.
- 20mm does not fall within the valid range of 3 < x < 17.
- 2mm does not fall within the valid range of 3 < x < 17.

Therefore, the length of the third side that is a valid option from the given choices is 5mm.