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Big Ideas Math Integrated I, 2016 View details

1. Angles of Triangles

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Exercise 36 Page 593

Consider the Exterior Angle Theorem.

140^(∘)

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From previous exercises, we know that the measure of ∠ 1 is 50^(∘).

According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. We see that ∠ 8 is exterior angle to the 40^(∘) angle of the larger triangle. Therefore, we can equate it's measure with the sum of the two nonadjacent angles, 50^(∘) and 90^(∘). m∠ 8=50^(∘)+90^(∘) By simplifying the equation, we can find the measure of ∠ 8.

m∠ 8=50^(∘)+90^(∘)

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m∠ 8=140^(∘)

The measure of ∠ 8 is 140^(∘).