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Use the figure to answer the question. Triangle A B C with angle of 45 degrees at C.© 2019 StrongMind. Created using GeoGebra. △ABC has a right angle, ∠ABC, and m∠BCA=45∘. Therefore, m∠CAB= [blank] −−−−−−∘.Enter the number that correctly fills in the blank.

Use the figure to answer the question. Triangle A B C with angle of 45 degrees at-example-1
User Rsakhale
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1 Answer

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45

Step-by-step explanation

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, to find the missin angle we can use the fact that the sum of the internal angles in a triangle equals 180 degrees, so

Step 1

given


\begin{gathered} m\measuredangle BCA=45 \\ m\angle CBA=90 \\ m\angle CAB=unknown \end{gathered}

so


\begin{gathered} sum\text{ of internal angles =}180 \\ replace \\ m\measuredangle BCA+m\measuredangle CBA+m\measuredangle CAB=180 \\ 45+90+m\measuredangle CAB=180 \\ 135+m\measuredangle CAB=180 \\ subtract\text{ 135 in both sides} \\ 135+m\operatorname{\measuredangle}CAB-135=180-135 \\ m\operatorname{\measuredangle}CAB=45\text{ \degree} \end{gathered}

therefore, the answer is

45

I hope this helps you

User Binaryorganic
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