Exercise 30 Page 593

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 ∠ 2 is exterior angle to ∠ 1. Therefore, we can equate it's measure with the sum of the two nonadjacent angles, 40^(∘) and 90^(∘). m∠ 2=90^(∘)+40^(∘). By simplifying the equation, we can find the measure of ∠ 2.

m∠ 2=90^(∘)+40^(∘)

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m∠ 2=130^(∘)

The measure of ∠ 2 is 130^(∘).