To find angle \( b \) using the properties of exterior angles of triangles, we start with an understanding of the exterior angle theorem. According to this theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Given the triangle, if you have an exterior angle measuring \( 142^\circ \), you can set up the equation as follows:
\[ \text{Exterior Angle} = \text{Interior Angle 1} + \text{Interior Angle 2} \]
If we denote the two remote interior angles of the triangle as \( a \) and \( b \), then:
\[ 142^\circ = a + b \]
To find angle \( b \), you would also need the measure of angle \( a \). If angle \( a \) is known (let's say \( a = x \)), you can rearrange the equation to find \( b \):
\[ b = 142^\circ - a \]
Without the specific value of angle \( a \), we cannot determine the precise value of angle \( b \). However, once you know \( a \), simply plug that value into \( b = 142^\circ - a \) to get angle \( b \). If you provide the value of angle \( a \) or more details about the triangle, I can help further!
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