In triangle XYZ, m∠Y = 62.45° and m∠Z = 41.8°. Determine the measure of the exterior angle to ∠X.

104.25°
75.75°
37.85°
18.94°

1 answer

To find the measure of the exterior angle to ∠X in triangle XYZ, we can first determine the measure of ∠X.

The sum of the interior angles in any triangle is 180°. Thus, we can find the measure of ∠X as follows:

\[ m∠X = 180° - m∠Y - m∠Z \]

Substituting the given angles:

\[ m∠X = 180° - 62.45° - 41.8° \]

Calculating this step-by-step:

  1. \( 62.45° + 41.8° = 104.25° \)
  2. \( 180° - 104.25° = 75.75° \)

Thus, \( m∠X = 75.75° \).

The measure of the exterior angle to ∠X is equal to the sum of the measures of the two non-adjacent interior angles in the triangle, which are ∠Y and ∠Z:

\[ m \text{ (exterior angle to } ∠X) = m∠Y + m∠Z \]

Calculating this:

\[ m \text{ (exterior angle to } ∠X) = 62.45° + 41.8° = 104.25° \]

Therefore, the measure of the exterior angle to ∠X is:

\[ \boxed{104.25°} \]