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Complete the statements below. The sum of the interior angle measures of a triangle must be []. So, m∠1 +...

Complete the statements below.
The sum of the interior angle measures of a triangle must be []. So, m∠1 + m∠2 + m∠4 = [].
We are given that m∠1 = 111° and m∠4 = 37°. Therefore, m∠1 + m∠4 = []. And so m∠2 = [].
From the figure, we can see that m∠2 + m∠3 = []. Using the value we already found for m∠2, we find that m∠3 = [].
Therefore, m∠3 [Select] m∠1 + m∠4.
This result is an example of the Exterior Angle Property of Triangles. For any triangle, the measure of an exterior angle [Select]

Answer

  1. The sum of the interior angle measures of a triangle must be 180°. So, m∠1 + m∠2 + m∠4 = 180°.
  2. We are given that m∠1 = 111° and m∠4 = 37°. Therefore, m∠1 + m∠4 = 148°. And so m∠2 = 32°.
  3. From the figure, we can see that m∠2 + m∠3 = 180°. Using the value we already found for m∠2, we find that m∠3 = 148°.
  4. Therefore, m∠3 equals m∠1 + m∠4.
  5. This result is an example of the Exterior Angle Property of Triangles. For any triangle, the measure of an exterior angle equals the sum of the two non-adjacent interior angles.

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