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Big Ideas Math Integrated I, 2016 View details

1. Angles of Triangles

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Exercise 34 Page 593

Consider the Exterior Angle Theorem.

140^(∘)

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From previous exercises, we know that the measure of ∠ 3 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 ∠ 6 is exterior angle to ∠ 3. Therefore, we can equate it's measure with the sum of the two nonadjacent angles, 50^(∘) and 90^(∘). m∠ 6=90^(∘)+50^(∘). By simplifying the equation, we can find the measure of ∠ 6.

m∠ 6=90^(∘)+50^(∘)

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m∠ 6=140^(∘)

The measure of ∠ 6 is 140^(∘).