Which combination of angle measures could form a triangle?

Question

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1 point
55°, 65°, and 75°
20°, 65°, and 75°
35°, 55°, and 90°
30°, 65°, and 95°

Answer 1

35°, 55°, and 90°

Answer 2

The angles of a triangle measure 2x, 4x, and 4x. Using the Triangle Angle Sum Theorem (Remember the sum of angles for all triangles is always 180 °). Find the measure of the smallest angle in this triangle.
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2 points
10°
120°
36°
72°

Answer 3

36°

The sum of the angles in a triangle is always 180°, so we have:

2x + 4x + 4x = 180
10x = 180
x = 18

Now we can find the measure of the smallest angle, which is 2x:
2(18) = 36°

Therefore, the measure of the smallest angle in this triangle is 36°.

Answer 4

Use the Triangle Sum Theorem to find the measure of angle a.
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2 points
Captionless Image
180°
72°
38°
70°

Answer 5

To find the measure of angle a, we can use the Triangle Sum Theorem which states that the sum of the interior angles in a triangle is always 180°.

In this case, we have angle a, 72°, and 70°. So, we can set up the equation:

a + 72 + 70 = 180

Combining like terms, we have:

a + 142 = 180

Subtracting 142 from both sides, we find:

a = 38°

So, the measure of angle a is 38°.

Answer 6

the image shows a being inside the top of the triangle showing a text that says a
and showing 70 inside the triangle on the bottom left and showing 142 outside the bottom right corner of the triangle and the floor of the triangle keeps going for a little bit outside the triangle

Answer 7

In the image you provided, you described angle a as being inside the top of the triangle, 70° inside the triangle on the bottom left, and 142° outside the bottom right corner of the triangle. Given this information, we can see that the exterior angle at the bottom right corner of the triangle is 142°, which is the supplement of the interior angle at the bottom right corner (which is 38°).

Therefore, the measure of angle a, which is the interior angle at the top of the triangle, would be equal to 180° minus the supplement of the exterior angle at the bottom right corner.

a = 180° - 142°
a = 38°

So, the measure of angle a is 38° in the triangle you described in the image.

Answer 8

Find the measure of the smallest angle of the triangle. Remember the sum of angles for all triangles is always 180 °.
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2 points
Captionless Image
102°
33°
45°
30°

Answer 9

To find the measure of the smallest angle in the triangle, we need to use the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180°.

Let's denote the angles of the triangle as x, y, and z. We are looking for the smallest angle, so we're looking for the smallest value among x, y, and z.

Given that two of the angles are 102° and 45°, we can set up the equation using the theorem:

x + 102 + 45 = 180

Combine like terms and solve for x:

x + 147 = 180
x = 180 - 147
x = 33

Therefore, the measure of the smallest angle of the triangle is 33°.

Answer 10

the captionless image shows 3x being inside the top of the triangle and 102 being inside the bottom left corner of the triangle and X+18 being inside the bottom right corner of the triangle.

Answer 11

If the triangle has angles denoted as 3x, 102, and x + 18, and the sum of all angles in a triangle is 180°, we can set up the equation based on the given information:

3x + 102 + (x + 18) = 180

Combine like terms:

4x + 120 = 180

Solve for x:

4x = 60
x = 15

Now substitute x back into the expressions for the angles:

3x = 3(15) = 45°
x + 18 = 15 + 18 = 33°

The angles are 45°, 102°, and 33°. To find the smallest angle among them, we determine it to be 33°.

Therefore, the measure of the smallest angle in the triangle is 33°.