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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
130^(∘)
We are given a triangle and asked to find the measure of the exterior angle.
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Exterior Angle Measures of a Triangle Theorem |
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. |
We will now identify the exterior angle and the two nonadjacent interior angles.
We can see that the measure of the exterior angle is j^(∘) and the measures of the nonadjacent interior angles are 90^(∘) and 40^(∘). By the Exterior Angle Measures of a Triangle Theorem, we can write an equation in terms of j. j^(∘)= 90^(∘)+ 40^(∘) Let's solve the equation! For simplicity, we will not write the degree symbol while solving. j=90+40 ⇔ j=130 The measure of the exterior angle is 130^(∘).