Question
Examine the diagram. It is not drawn to scale.
Triangle X Y Z. Angle X is 50 degrees, angle Z is 75 degrees, and angle Y is 55 degrees. Side Y Z extends to form angle 3.
What is the mAngle3?
mAngle3 =
°
Triangle X Y Z. Angle X is 50 degrees, angle Z is 75 degrees, and angle Y is 55 degrees. Side Y Z extends to form angle 3.
What is the mAngle3?
mAngle3 =
°
Answers
GPT-4o mini
To find the measure of angle 3, we can use the fact that the sum of angles around a point is 360 degrees.
Angle 3 is formed by extending side YZ of triangle XYZ, which means angle 3 is the exterior angle at vertex Y. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
In triangle XYZ:
- m∠X = 50 degrees
- m∠Y = 55 degrees
- m∠Z = 75 degrees
To find mAngle 3:
\[
mAngle3 = m∠X + m∠Z = 50° + 75° = 125°
\]
Thus, the measure of angle 3 is:
\[
\text{mAngle3} = 125°.
\]
Angle 3 is formed by extending side YZ of triangle XYZ, which means angle 3 is the exterior angle at vertex Y. The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
In triangle XYZ:
- m∠X = 50 degrees
- m∠Y = 55 degrees
- m∠Z = 75 degrees
To find mAngle 3:
\[
mAngle3 = m∠X + m∠Z = 50° + 75° = 125°
\]
Thus, the measure of angle 3 is:
\[
\text{mAngle3} = 125°.
\]