Bot GPT 4-o mini To find angle \( b \) using the property of exterior angles in a triangle, you can use the following relationship:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle at angle \( a \) is given as \( 142^\circ \).
The angles in the triangle are:
- Exterior angle: \( 142^\circ \)
- Interior angle \( a \)
- Interior angle \( b \)
According to the property of exterior angles: \[ \text{Exterior angle} = \text{Interior angle } a + \text{Interior angle } b \] This can be written as: \[ 142^\circ = a + b \]
Also, since this is a right triangle, we know that: \[ a + b = 90^\circ \]
Now, we can substitute \( 90^\circ \) for \( a + b \) in the exterior angle equation: \[ 142^\circ = 90^\circ + b \]
To isolate \( b \), we subtract \( 90^\circ \) from both sides: \[ b = 142^\circ - 90^\circ \] \[ b = 52^\circ \]
Thus, angle \( b \) is \( 52^\circ \).
Therefore, the correct response is: 52°
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