Use the properties of exterior angles of triangles to find angle b

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92°
92 degrees

38°
38 degrees

232°
232 degrees

52°
52 degrees
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1 answer

To find angle \( b \) using the properties of exterior angles of triangles, you need to recall that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.

If you have an exterior angle formed by extending one side of the triangle, let's denote it as angle \( E \). Then, according to the exterior angle theorem:

\[ E = a + b \]

where \( a \) and \( b \) are the two opposite interior angles adjacent to angle \( E \).

If we know the value of angle \( E \) and one of the interior angles, we can rearrange the formula to find the unknown angle:

\[ b = E - a \]

Without the numerical values for either \( E \) or \( a \) from your question, it's not possible to definitively solve for angle \( b \). If you can provide the values for the exterior angle and either of the interior angles, I'd be happy to help you determine the value of angle \( b \).