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The sum of the measures of the interior angles of a triangle is 180^(∘).
Possible Values: 90^(∘), 135^(∘)
Explanation: See solution.
Therefore, the interior angles of Maggie's triangle have measures 90^(∘), 45^(∘), and 45^(∘). Since we know the values of all the interior angles, we can draw Maggie's triangle!
Now let's draw an extension of each side of the triangle and mark the exterior angles of the triangle. Recall that an exterior angle of a triangle is an angle formed by a side and an extension of an adjacent side.
Next, we will find m∠ 1, m∠ 2, and m∠ 3. Note that ∠ 1 and the right angle form a straight angle and are supplementary. Using this fact, we can calculate m∠ 1. m∠ 1 + 90^(∘) = 180^(∘) [0.4em] ⇕ [0.4em] m∠ 1 = 180^(∘) - 90^(∘) = 90^(∘) Similarly, ∠ 2 is supplementary to the 45^(∘) angle and ∠ 3 is supplementary to the 45^(∘) angle. Let's calculate m∠ 2 using this fact! m∠ 2 + 45^(∘) = 180^(∘) [0.4em] ⇕ [0.4em] m∠ 2 = 180^(∘) - 45^(∘) = 135^(∘) Finally, we will find m∠ 3. m∠ 3 + 45^(∘) = 180^(∘) [0.4em] ⇕ [0.4em] m∠ 3 = 180^(∘) - 45^(∘) = 135^(∘) Therefore, the possible values of the exterior angles for Maggie's triangle are 90^(∘) and 135^(∘).
