Question
Create a right triangle, in which A is the right angle, and m∠C is approximately 60°.
What is the approximate measure of AngleB?
mAngleB =
°
What is the sum of mAngleA, mAngleB, and mAngleC?
°
Answers
GPT-4o mini
In a right triangle, one of the angles is always 90 degrees (Angle A in this case). If \( m\angle C \) is approximately 60 degrees, we can find the measure of Angle B using the fact that the sum of the angles in a triangle is always 180 degrees.
Given:
- \( m\angle A = 90^\circ \)
- \( m\angle C \approx 60^\circ \)
We can calculate \( m\angle B \) as follows:
\[
m\angle A + m\angle B + m\angle C = 180^\circ
\]
\[
90^\circ + m\angle B + 60^\circ = 180^\circ
\]
\[
m\angle B + 150^\circ = 180^\circ
\]
\[
m\angle B = 180^\circ - 150^\circ
\]
\[
m\angle B = 30^\circ
\]
So,
\[
m\angle B \approx 30^\circ
\]
Now, we'll calculate the sum of the angles:
\[
m\angle A + m\angle B + m\angle C = 90^\circ + 30^\circ + 60^\circ = 180^\circ
\]
Therefore, the measures are:
- \( m\angle B \approx 30^\circ \)
- The sum \( m\angle A + m\angle B + m\angle C = 180^\circ \)
Given:
- \( m\angle A = 90^\circ \)
- \( m\angle C \approx 60^\circ \)
We can calculate \( m\angle B \) as follows:
\[
m\angle A + m\angle B + m\angle C = 180^\circ
\]
\[
90^\circ + m\angle B + 60^\circ = 180^\circ
\]
\[
m\angle B + 150^\circ = 180^\circ
\]
\[
m\angle B = 180^\circ - 150^\circ
\]
\[
m\angle B = 30^\circ
\]
So,
\[
m\angle B \approx 30^\circ
\]
Now, we'll calculate the sum of the angles:
\[
m\angle A + m\angle B + m\angle C = 90^\circ + 30^\circ + 60^\circ = 180^\circ
\]
Therefore, the measures are:
- \( m\angle B \approx 30^\circ \)
- The sum \( m\angle A + m\angle B + m\angle C = 180^\circ \)