Angles of Triangles Quick Check
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Question
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)
Responses
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 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.
To find the third angle of a triangle, you can use the fact that the sum of the angles in a triangle always adds up to 180°. Given that you already have two angles of 22° and 46°, you can calculate the third angle as follows:
Third angle = 180° - (22° + 46°)
Third angle = 180° - 68°
Third angle = 112°
Now that you know the third angle measure is 112°, you can establish the type of triangle based on its angles. A triangle is classified as follows:
- Acute triangle: All angles are less than 90°.
- Right triangle: One angle is exactly 90°.
- Obtuse triangle: One angle is greater than 90°.
Since the third angle measure is 112°, which is greater than 90°, it follows that the triangle is an obtuse triangle.
Therefore, the correct response is:
The third angle measure is 112°, and the triangle is an obtuse triangle.
Can a triangle have two right angles, and why or why not?(1 point)
Responses
No, because there needs to be a third angle.
No, because there needs to be a third angle.
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.
No, a triangle cannot have two right angles. The sum of the angles in a triangle must always be 180°. If a triangle had two right angles, each being 90°, the sum of just those two angles would already be 180°. This leaves no room for a third angle, as required by the definition of a triangle, which must have three angles.
The sum of two right angles:
90° + 90° = 180°
This would imply that the third angle has no degree measure left, which is not possible. A triangle must have three angles, and all three angles must add up to 180°.
Therefore, 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
To determine the type of triangle based on the given angles, we must consider the three possible classifications:
- Acute triangle: All angles are less than 90°.
- Right triangle: One angle is exactly 90°.
- Obtuse triangle: One angle is greater than 90°.
Given the angles 46°, 51°, and 83°:
- None of the angles are exactly 90°, so it is not a right triangle.
- None of the angles are greater than 90°, so it is not an obtuse triangle.
Since all angles are less than 90°:
- The triangle is an acute triangle because all of its angles (46°, 51°, and 83°) are less than 90°.
So, the triangle with angles measuring 46°, 51°, and 83° is an acute triangle.
Use the properties of exterior angles of triangles to find angle b .
(1 point)
Responses
92°
92 degrees
232°
232 degrees
52°
52 degrees
38°
To properly answer this question, I would need the precise context of the given problem, including the relationship between angle b and the other angles of the triangle, or a diagram showing angle b and its position relative to the triangle.
If we are talking about the exterior angle theorem, the exterior angle of a triangle is equal to the sum of the two opposite interior angles. Here's a general example of how it works:
Consider triangle ABC with an exterior angle at vertex C, which we'll call angle b. Let's say the two interior angles at vertices A and B are angle A and angle B respectively.
By the exterior angle theorem:
angle b = angle A + angle B
Without the specific angles provided for the triangle you're referring to, I can't calculate the measurement of angle b. If you have values for the two non-adjacent interior angles or other related measurements, please provide them, so I can give you an accurate response for angle b.