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# Triangles

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In the figure, BA = AD = DC and point D is on segment BC. The measure of angle ACD is 25 degrees. What is the measure of angle ABC?

Jun 2, 2021

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Both of the separate triangles in this figure are isosceles, as two of their sides are the same.

Thus, we know that $\angle{ACD} = \angle{DAC} = 25$.

From this, we know that $\angle{ADC} = 180 - 25 \cdot 2$, for the two other angles in the triangle. Thus, $\angle{ADC} = 130$.

Because $\angle{ADB}$ and $\angle{ADC}$ are supplementary, we know that $\angle{ADB} = 180 - 130 = 50$.

Finally, since $\triangle{ABD}$ is isosceles, we know that $\angle{ABC}$ is also $\boxed{50}$.

Jun 2, 2021