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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∠3 = [].
We are given that m∠3 = 57°.
So, m∠1 + m∠2 = [].
From the figure, we can see that m∠3 + m∠4 = [].
Since m∠3 = 57°, it must be that m∠4 = [].
Therefore, m∠4 [] m∠1 + m∠2.
This result is an example of the Exterior Angle Property of Triangles.
For any triangle, the measure of an exterior angle

Answer

  1. The sum of the interior angle measures of a triangle must be 180°.
  2. So, m∠1 + m∠2 + m∠3 = 180°.
  3. We are given that m∠3 = 57°.
  4. So, m∠1 + m∠2 = 123°.
  5. From the figure, we can see that m∠3 + m∠4 = 180°.
  6. Since m∠3 = 57°, it must be that m∠4 = 123°.
  7. Therefore, m∠4 equals m∠1 + m∠2.

This result is an example of the Exterior Angle Property of Triangles. For any triangle, the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.

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