2. In the figure, is an exterior angle to .

(a) Explain why is equal to the sum of the measures of the two nonadjacent interior angles. ***What is the name of the property? ***
there is another question look at the image for the second one!

Part A. The name of this property is Triangle Exterior Angle Theorem, that states that an exterior angle of any triangle is equal to the sum of the opposite interior angles.

Part B. m ∠ 4 = 77°

Explanation:

Part A. Let's recall that:

i: The interior angles of any triangle always add up to 180 degrees, therefore in our case:

∠1 + ∠2 + ∠3 = 180°, thus:

∠3 = 180 - ∠1 + ∠2

Replacing with the values we have:

∠3 = 180 - 57 - 20

∠3 = 103°

ii. ∠3 + ∠4 are supplementary angles, because they add up to 180 degrees, in consequence:

∠3 + ∠4 = 180 °

Replacing with the values we have:

∠4 = 180 - ∠3

∠4 = 180 - 103

∠4 = 77 and we can substitute 77 by ∠1 + ∠2, then:

∠4 = ∠1 + ∠2

77 = 57 + 20

The name of this property is Triangle Exterior Angle Theorem, that states that an exterior angle of any triangle is equal to the sum of the opposite interior angles.

Part B. m ∠ 4 = 77°

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