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Big Ideas Math Integrated I, 2016 View details

1. Angles of Triangles

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Exercise 16 Page 592

Consider the Exterior Angle Theorem.

92^(∘)

Practice makes perfect

Let's analyze the given triangle.

We can see that the interior angles are x^(∘) and 45^(∘). 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. This allows us to write an equation. 2x-2=x+45 We will now solve the above equation for x.

2x-2=x+45

SubEqn

LHS-x=RHS-x

x-2=45

AddEqn

LHS+2=RHS+2

x=47

Now we can substitute x= 47 in the expression 2x-2 to find the measure of the angle. 2( 47)-2=92^(∘) Therefore, the measure of the exterior angle is 92^(∘).