Two angles 2

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

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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