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)
Responses
The third angle measure is 112°, and the triangle is an obtuse triangle.
The third angle measure is 112 degrees , and the triangle is an obtuse 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 acute triangle.
The third angle measure is 112 degrees , and the triangle is an acute triangle.
The third angle measure is 68°, and the triangle is an obtuse triangle.
In a triangle, the sum of the angles must always equal 180 degrees. Given that one angle is 22° and the other is 46°, we can calculate the third angle as follows:
22° + 46° + Third angle = 180°
68° + Third angle = 180°
Third angle = 180° - 68°
Third angle = 112°
The third angle is 112°. Given that none of the angles in the triangle are above 90°, the triangle is an acute triangle, as all angles are less than 90°.
So the correct statement is:
The third angle measure is 112°, and the triangle is an acute triangle.
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 there needs to be a third angle.
No, because there needs to be a third angle.
No, because a triangle must have an obtuse angle.
No, because a triangle must have an obtuse angle.
Yes, because 90 + 90 = 180.
A triangle cannot have two right angles. This is because if a triangle had two right angles (each measuring 90 degrees), the sum of those two angles would already be 180 degrees. Since the sum of all the angles in any triangle must be exactly 180 degrees, there would be no degrees left for the third angle, which is impossible as every angle in a triangle must have a positive measure.
Hence, the correct response is:
No, because there needs to be a third angle.
If a triangle has angles measuring 46°, 51°, and 83°, what type of triangle is it?(1 point)
Responses
right triangle
right triangle
obtuse triangle
obtuse triangle
small triangle
small triangle
acute triangle
To determine the type of triangle based on its angle measurements, we need to consider the size of the angles:
- A right triangle has one angle that is exactly 90°.
- An obtuse triangle has one angle that is greater than 90°.
- An acute triangle has all angles less than 90°.
Given the angles 46°, 51°, and 83°, none of these angles are 90° or greater than 90°. Therefore, the triangle with these angles is not a right triangle nor an obtuse triangle. All the angles are less than 90°, so the triangle is an acute triangle.
The correct response is:
acute triangle
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
52°
52 degrees
38°
38 degrees
232°
232 degrees
92°
In a triangle, an exterior angle is equal in measure to the sum of the two opposite interior angles. In the case of a right triangle with an exterior angle formed at angle a, this exterior angle will be equal to angle a + angle b (where angle b is the other non-right interior angle).
Given that the right angle is 90° and the exterior angle is 142°, we can set up the following equation:
Exterior angle = angle a + angle b
142° = 90° + angle b
Now we can solve for angle b:
angle b = 142° - 90°
angle b = 52°
Therefore, angle b measures 52 degrees.
The correct response is:
52°
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
38°
38 degrees
52°
52 degrees
142°
142 degrees
128°
An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. The description states that there is an exterior angle of 38 degrees at vertex H of triangle HIJ, which means that this angle is equal to the sum of the interior angles at vertices I and J.
Let's call the interior angle at vertex I angle I and the interior angle at vertex J angle J. According to the exterior angle theorem:
angle I + angle J = exterior angle at vertex H
angle I + angle J = 38 degrees
This question, however, contains an inconsistency because, normally, an exterior angle cannot be smaller than any of the remote interior angles it's associated with in a triangle. It seems that the exterior angle measure at vertex H (38 degrees) is not consistent with typical geometric principles. Normally, if an exterior angle were 38 degrees, the sum of the interior angles at I and J would have to be larger than 38 degrees.
Assuming the description of the exterior angle as being 38 degrees is a mistake and that it should apply to either angle I or angle J, then the sum of angle I and angle J would be:
180 degrees - 38 degrees = 142 degrees
(because the interior angles of a triangle always add up to 180 degrees)
Therefore, under normal circumstances, the sum of the interior angles at vertex I and vertex J would be 142 degrees. However, this relies on the assumption that the measure provided for the exterior angle was intended for one of the interior angles instead. If the information provided is accurate and without error, then there may be a mistake in the question as provided. Without a visual image to clarify, we can only provide an answer based on typical geometric principles, which give a sum of 142 degrees for the two interior angles.