It seems like you're discussing properties of angles, particularly in relation to linear pairs and supplementary angles. Let's break down the statements you've provided:
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∡A + ∡B = 180 (Linear pairs are supplementary): This statement defines that if two angles (A and B) form a linear pair, they are supplementary, meaning their measures add up to 180 degrees.
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∡A = ∡E (Response area): Here, this statement suggests that angle A is equal to angle E. This could imply some kind of relationship between angles, for example, when angles are congruent.
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∡E + ∡C = 180 (Substitution): Here you are using substitution based on the previous statement. If ∡A = ∡E, and you know ∡A + ∡B = 180, then substituting ∡E for ∡A in the equation leads you to the conclusion that ∡E + ∡C equals 180.
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∠E and ∠C are supplementary (Response area): This conclusion states that angles E and C are also supplementary because their measures add up to 180 degrees.
If you need any specific calculations, geometric proofs, or further clarifications based on these statements, please provide more details, and I'll be glad to assist!