Question
What must the angles in a triangle add up to?(1 point)
°
2. If a triangle has a 32° angle and a 67° angle, what is the measurement of the third angle?(1 point)
3. If two angles of a triangle add up to 110, what is the measure of the third angle?
4. a scalene triangle it seems with 40 and 30 degrees find the x figure.
5. an acute traingle it seems with 50 and 70 degrees find the d figure.
°
2. If a triangle has a 32° angle and a 67° angle, what is the measurement of the third angle?(1 point)
3. If two angles of a triangle add up to 110, what is the measure of the third angle?
4. a scalene triangle it seems with 40 and 30 degrees find the x figure.
5. an acute traingle it seems with 50 and 70 degrees find the d figure.
Answers
Answered by
GPT-4o mini
1. The angles in a triangle add up to **180°**.
2. To find the measurement of the third angle in a triangle with a 32° angle and a 67° angle, you subtract the sum of the two angles from 180°:
\[
180° - (32° + 67°) = 180° - 99° = 81°
\]
So, the third angle is **81°**.
3. If two angles of a triangle add up to 110°, the measure of the third angle can be calculated as follows:
\[
180° - 110° = 70°
\]
Therefore, the third angle is **70°**.
4. In a scalene triangle with angles of 40° and 30°, the measure of the third angle \( x \) can be calculated like this:
\[
x = 180° - (40° + 30°) = 180° - 70° = 110°
\]
Therefore, the third angle \( x \) is **110°**.
5. In an acute triangle with angles of 50° and 70°, the measure of the third angle \( d \) can be calculated as follows:
\[
d = 180° - (50° + 70°) = 180° - 120° = 60°
\]
Thus, the third angle \( d \) is **60°**.
2. To find the measurement of the third angle in a triangle with a 32° angle and a 67° angle, you subtract the sum of the two angles from 180°:
\[
180° - (32° + 67°) = 180° - 99° = 81°
\]
So, the third angle is **81°**.
3. If two angles of a triangle add up to 110°, the measure of the third angle can be calculated as follows:
\[
180° - 110° = 70°
\]
Therefore, the third angle is **70°**.
4. In a scalene triangle with angles of 40° and 30°, the measure of the third angle \( x \) can be calculated like this:
\[
x = 180° - (40° + 30°) = 180° - 70° = 110°
\]
Therefore, the third angle \( x \) is **110°**.
5. In an acute triangle with angles of 50° and 70°, the measure of the third angle \( d \) can be calculated as follows:
\[
d = 180° - (50° + 70°) = 180° - 120° = 60°
\]
Thus, the third angle \( d \) is **60°**.
Answer
okay you got 4 and 5 wrong
4. 75
5. 120
Angles of triangle quick check:
If a triangle has a 22°
22
°
angle and a 46°
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°
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°
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°
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°
68
°
, and the triangle is an obtuse triangle.
2. Can a triangle have two right angles, and why or why not?(1 point)
Responses
Yes, because 90 + 90 = 180
90
+
90
=
180
.
Yes, because 90 plus 90 equals 180 .
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 it would be a right triangle.
Yes, because it would be a right triangle.
3. If a triangle has angles measuring 46°
46
°
, 51°
51
°
, and 83°
83
°
, what type of triangle is it?(1 point)
Responses
obtuse triangle
obtuse triangle
acute triangle
acute triangle
right triangle
right triangle
small triangle
4. 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)Responses92°92 degrees52° 38°
38
°
38 degrees
232°
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
𝐼
and vertex J
𝐽
?
(1 point)
Responses
38°
38
°
38 degrees
52°
52
°
52 degrees
128°
128
°
128 degrees
142°
142
°
142 degrees
4. 75
5. 120
Angles of triangle quick check:
If a triangle has a 22°
22
°
angle and a 46°
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°
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°
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°
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°
68
°
, and the triangle is an obtuse triangle.
2. Can a triangle have two right angles, and why or why not?(1 point)
Responses
Yes, because 90 + 90 = 180
90
+
90
=
180
.
Yes, because 90 plus 90 equals 180 .
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 it would be a right triangle.
Yes, because it would be a right triangle.
3. If a triangle has angles measuring 46°
46
°
, 51°
51
°
, and 83°
83
°
, what type of triangle is it?(1 point)
Responses
obtuse triangle
obtuse triangle
acute triangle
acute triangle
right triangle
right triangle
small triangle
4. 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)Responses92°92 degrees52° 38°
38
°
38 degrees
232°
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
𝐼
and vertex J
𝐽
?
(1 point)
Responses
38°
38
°
38 degrees
52°
52
°
52 degrees
128°
128
°
128 degrees
142°
142
°
142 degrees
Answered by
GPT-4o mini
Let's go through the questions one by one based on the information provided.
1. **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?**
To find the third angle:
\[
\text{Third angle} = 180° - (22° + 46°) = 180° - 68° = 112°
\]
Since 112° is greater than 90°, the triangle is an **obtuse triangle**.
Therefore, the correct response is: **The third angle measure is 112°, and the triangle is an obtuse triangle.**
2. **Can a triangle have two right angles, and why or why not?**
The answer is: **No, because there needs to be a third angle.**
A triangle's angles must add up to 180°. If there are two right angles (90° each), that totals 180° already, leaving no room for a third angle.
3. **If a triangle has angles measuring 46°, 51°, and 83°, what type of triangle is it?**
The angles are:
46° + 51° + 83° = 180° (Which is valid for a triangle)
Since all angles are less than 90°, the triangle is an **acute triangle**.
So the correct response is: **acute triangle**.
4. **If the exterior angle is 142°, how do we find angle b?**
The exterior angle is equal to the sum of the two remote interior angles. In a right triangle, the other two angles are complementary:
\[
b + 90° = 142° \implies b = 142° - 90° = 52°
\]
Thus, the correct response is: **52°**.
5. **If the exterior angle at vertex H is 38°, what is the sum of the interior angles at vertices I and J?**
The exterior angle is equal to the sum of the non-adjacent interior angles:
\[
38° = I + J
\]
Therefore, the sum of the measures of the interior angles at vertices I and J is equal to **38°**.
So the correct response is: **38°**.
Feel free to ask more questions or for clarifications!
1. **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?**
To find the third angle:
\[
\text{Third angle} = 180° - (22° + 46°) = 180° - 68° = 112°
\]
Since 112° is greater than 90°, the triangle is an **obtuse triangle**.
Therefore, the correct response is: **The third angle measure is 112°, and the triangle is an obtuse triangle.**
2. **Can a triangle have two right angles, and why or why not?**
The answer is: **No, because there needs to be a third angle.**
A triangle's angles must add up to 180°. If there are two right angles (90° each), that totals 180° already, leaving no room for a third angle.
3. **If a triangle has angles measuring 46°, 51°, and 83°, what type of triangle is it?**
The angles are:
46° + 51° + 83° = 180° (Which is valid for a triangle)
Since all angles are less than 90°, the triangle is an **acute triangle**.
So the correct response is: **acute triangle**.
4. **If the exterior angle is 142°, how do we find angle b?**
The exterior angle is equal to the sum of the two remote interior angles. In a right triangle, the other two angles are complementary:
\[
b + 90° = 142° \implies b = 142° - 90° = 52°
\]
Thus, the correct response is: **52°**.
5. **If the exterior angle at vertex H is 38°, what is the sum of the interior angles at vertices I and J?**
The exterior angle is equal to the sum of the non-adjacent interior angles:
\[
38° = I + J
\]
Therefore, the sum of the measures of the interior angles at vertices I and J is equal to **38°**.
So the correct response is: **38°**.
Feel free to ask more questions or for clarifications!