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In every triangle, an exterior angle = sum of the . . . . interior opposite angles.

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To solve the question, we need to fill in the blank in the statement: "In every triangle, an exterior angle = sum of the . . . . interior opposite angles." ### Step-by-Step Solution: 1. **Understanding the Triangle and Exterior Angle**: - Let's consider a triangle ABC. The exterior angle is formed when one side of the triangle is extended. For example, if we extend side BC, we create an exterior angle at vertex A. 2. **Labeling the Angles**: - In triangle ABC, let angle A be ∠A, angle B be ∠B, and angle C be ∠C. The exterior angle formed at vertex A when side BC is extended is called angle Y. 3. **Using the Triangle Angle Sum Property**: - We know that the sum of the interior angles of triangle ABC is: \[ \angle A + \angle B + \angle C = 180^\circ \] 4. **Relating the Exterior Angle to the Interior Angles**: - The exterior angle Y can be expressed in terms of the interior angles. Specifically, angle Y is equal to the sum of the two opposite interior angles, which are ∠B and ∠C. Therefore, we can write: \[ Y = \angle B + \angle C \] 5. **Filling in the Blank**: - From the relationship we derived, we conclude that in every triangle, an exterior angle is equal to the sum of the two interior opposite angles. Thus, we fill in the blank with "two": \[ \text{In every triangle, an exterior angle = sum of the } \textbf{two} \text{ interior opposite angles.} \] ### Final Answer: In every triangle, an exterior angle = sum of the **two** interior opposite angles.
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