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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.
We want to find the possible values of the exterior angles for Maggie's triangle. Let's start by finding the measures of the interior angles for the triangle. We know that the triangle has a right angle and the other two angles have equal measures. Recall that the sum of the measures of the interior angles of a triangle is 180^(∘). Let's use this property for Maggie's triangle! 90^(∘) + x^(∘) + x^(∘) = 180^(∘) Now we can solve the obtained equation for x.
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^(∘).
