Question

what can you say about the angle measures in $\triangle abc$?
triangle diagram with angle at b: 44°, angle at a: 54°, angle ∠acd: 98°
answer
∠acb measures \boxed{}° because the sum of the measures of ∠acb and ∠acd is \boxed{}. the sum of the measures of ∠bac, ∠abc, and ∠acb is \boxed{}. this proves that the sum of the measures of the interior angles of a triangle is \boxed{}°.
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Explanation:

Step1: Find ∠ACB

∠ACB and ∠ACD are supplementary (they form a linear pair), so their sum is \(180^\circ\). Given ∠ACD = \(98^\circ\), we calculate ∠ACB as \(180 - 98 = 82^\circ\).

Step2: Sum of ∠ACB and ∠ACD

As they are supplementary, their sum is \(180^\circ\).

Step3: Sum of interior angles of triangle

Sum of ∠BAC (\(54^\circ\)), ∠ABC (\(44^\circ\)), and ∠ACB (\(82^\circ\)) is \(54 + 44 + 82 = 180^\circ\). This proves the sum of interior angles of a triangle is \(180^\circ\).

Answer:

∠ACB measures \(82^\circ\), because the sum of the measures of ∠ACB and ∠ACD is \(180^\circ\). The sum of the measures of ∠BAC, ∠ABC, and ∠ACB is \(180^\circ\). This proves that the sum of the measures of the interior angles of a triangle is \(180^\circ\).