Asked by bot gpt v 3.5

If a triangle has a 22° angle and a 46° angle, what can be established about the third angle measure and the type of triangle?(1 point

The third angle measure is 68°, and the triangle is an obtuse triangle.
The third angle measure is 68 degrees , and the triangle is an obtuse triangle.

The third angle measure is 112°, and the triangle is an acute triangle.
The third angle measure is 112 degrees , and the triangle is an acute triangle.

The third angle measure is 128°, and the triangle is an obtuse triangle.
The third angle measure is 128 degrees , and the triangle is an obtuse triangle.

The third angle measure is 112°, and the triangle is an obtuse triangle.
Answered by bot gpt v 3.5
Can a triangle have two right angles, and why or why not?(1 point)
Responses

Yes, because it would be a right triangle.
Yes, because it would be a right triangle.

No, because a triangle must have an obtuse angle.
No, because a triangle must have an obtuse angle.

Yes, because 90 + 90 = 180.
Yes, because 90 plus 90 equals 180 .

No, because there needs to be a third angl
Answered by bot gpt v 3.5
If a triangle has angles measuring 46° , 51° , and 83° , what type of triangle is it?(1 point)
Responses

right triangle
right triangle

small triangle
small triangle

acute triangle
acute triangle

obtuse triangle
Answered by bot gpt v 3.5
Use the image to answer the question.



An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.
Use the properties of exterior angles of triangles to find angle b .

(1 point)
Responses

92°
92 degrees

52°
52 degrees

232°
232 degrees

38°
38 degrees
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Answered by bot gpt v 3.5
Use the image to answer the question.

An illustration shows triangle uppercase H uppercase I uppercase J. Uppercase H is the left vertex, uppercase I is the top vertex, and uppercase J is the right vertex. A line extending outward from uppercase H forms an exterior angle of 38 degrees.

What is the sum of the measures of the interior angles at vertex I and vertex J?

(1 point)
Responses

142°
142 degrees

52°
52 degrees

38°
38 degrees

128°
128 degrees
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Answered by GPT-4o mini
In a triangle, the sum of all angles is always 180°.

Given that you have a 22° angle and a 46° angle, you can calculate the third angle as follows:

\[
\text{Third angle} = 180° - (22° + 46°) = 180° - 68° = 112°
\]

Now, let's analyze the type of triangle based on the angles:

- An **acute triangle** has all angles less than 90°.
- A **right triangle** has one angle exactly equal to 90°.
- An **obtuse triangle** has one angle greater than 90°.

Since the third angle is 112°, which is greater than 90°, the triangle is classified as an **obtuse triangle**.

Therefore, the correct conclusion is:

**The third angle measure is 112°, and the triangle is an obtuse triangle.**
Answered by GPT-4o mini
No, a triangle cannot have two right angles. The reasons are as follows:

1. The sum of the angles in any triangle must equal 180°.
2. If a triangle had two right angles, that would mean:

\[
90° + 90° = 180°
\]

This equation would imply that there is no remaining angle left for the third angle, which is required for it to be a triangle.

3. Therefore, it is impossible to construct a triangle with two right angles.

Thus, the correct response is:

**No, because there needs to be a third angle.**
Answered by GPT-4o mini
To determine the type of triangle based on its angles (46°, 51°, and 83°), we can classify it as follows:

- An **acute triangle** has all angles measuring less than 90°.
- A **right triangle** has one angle exactly equal to 90°.
- An **obtuse triangle** has one angle greater than 90°.

In this case:

- 46° is less than 90° (acute)
- 51° is less than 90° (acute)
- 83° is also less than 90° (acute)

Since all three angles are less than 90°, the triangle is classified as an **acute triangle**.

Therefore, the correct response is:

**acute triangle**
Answered by GPT-4o mini
To find angle \( b \) in the triangle based on the information given, we can use the property of exterior angles of triangles. The exterior angle is equal to the sum of the two non-adjacent interior angles.

Given that the exterior angle is \( 142° \) and the interior angles are \( a \) and \( b \), we can write the equation:

\[
\text{Exterior angle} = a + b
\]

So we have:

\[
142° = a + b
\]

In a right triangle, one of the angles is \( 90° \). Assuming angle \( a \) is the right angle, we need to solve for \( b \):

Since angle \( a \) must be \( 90° \) (because it's a right triangle):

Substituting \( a \) into the equation gives us:

\[
142° = 90° + b
\]

To find \( b \), subtract \( 90° \) from \( 142° \):

\[
b = 142° - 90° = 52°
\]

Thus, angle \( b \) measures \( 52° \).

The correct response is:

**52°**
Answered by GPT-4o mini
In any triangle, the exterior angle at a vertex is equal to the sum of the two non-adjacent interior angles. In this case, the exterior angle at vertex \( H \) is given as \( 38° \).

Let \( I \) and \( J \) be the other two vertices of the triangle. According to the property of exterior angles, we can set up the following equation:

\[
\text{Exterior angle} = \text{Interior angle at I} + \text{Interior angle at J}
\]

Given that the exterior angle is \( 38° \):

\[
38° = \text{Angle at I} + \text{Angle at J}
\]

To find the sum of the measures of the interior angles at vertex \( I \) and vertex \( J \), we can express it as:

\[
\text{Angle at I} + \text{Angle at J} = 38°
\]

Since we need the sum of the angles at vertices \( I \) and \( J \), we can directly conclude that:

The sum of the measures of the interior angles at vertex \( I \) and vertex \( J \) is \( 38° \).

Thus, the correct response is:

**38°**