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Triangle \triangle ABC△ABCtriangle, A, B, C is reflected across line nnn to create \triangle A'B'C'△A
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B
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C
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triangle, A, prime, B, prime, C, prime.
A triangle A B C. The length of side CA is sixty one units. The angle B is sixty seven degrees. The line n is to the right of triangle A B C. Triangle A prime B prime C prime is the image of triangle A B C after being reflected across line n. The length of side C prime B prime is fifty seven units. Angle A prime is fifty nine degrees.





A triangle A B C. The length of side CA is sixty one units. The angle B is sixty seven degrees. The line n is to the right of triangle A B C. Triangle A prime B prime C prime is the image of triangle A B C after being reflected across line n. The length of side C prime B prime is fifty seven units. Angle A prime is fifty nine degrees.
What is the measure of \angle C∠Cangle, C?

Triangle Triangle ABCABCtriangle A B C Is Reflected Across Line Nnn To Create Triangle ABCA B C Triangle A Prime B Prime C Prime A Triangle A B C The Length Of class=

Sagot :

Medunno13

Answer: [tex]54^{\circ}[/tex]

Step-by-step explanation:

Because reflections are rigid motions, we know that [tex]\triangle ABC \cong \triangle A'B'C'[/tex], and thus [tex]\angle B \cong \angle B'[/tex].

It follows that since angles in a triangle add to 180 degrees, [tex]m\angle C'=180^{\circ}-59^{\circ}-67^{\circ}=\boxed{54^{\circ}}[/tex]

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