Two angles 2

Two angles of a triangle have the same measure, and the third one is 45 degrees greater than the measure of the other two. Find the measure of the largest angle in the triangle.

Final Answer:

x =  90 °

Step-by-step explanation:

$$\begin{gathered} \alpha +\beta +\gamma =180{}^{\circ } \\ \alpha =\beta \\ \gamma =45+\alpha \\ \alpha +\alpha +45+\alpha =180 \\ 3\alpha =180-45 \\ \alpha =\frac{180-45}{3}=45{}^{\circ } \\ \beta =\alpha =45=45{}^{\circ } \\ \gamma =45+\alpha =45+45=90{}^{\circ } \\ x=\gamma =90=90^{\circ } \end{gathered}$$

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