In triangle GHI, m∠H is 20 more than m∠G, and m∠G is 8 more than m∠I. What is the measure of each angle? Please show work

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In triangle GHI, m∠H is 20 more than m∠G, and m∠G is 8 more than m∠I. What is the measure of each angle? Please show work

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Eva 3 weeks 2021-11-16T05:49:50+00:00 1 Answer 0 views 0

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    2021-11-16T05:50:50+00:00

    Let \hat{G}, \hat{H}, \hat{I} be the measures of the angles. We know that \hat{H} = \hat{G}+20 and \hat{G} = \hat{I}+8.

    Moreover, we know that the sum of the interior angles of a triangle is 180:

    \hat{H} + \hat{G}+\hat{I}=180

    So, we have the following system:

    \begin{cases}\hat{H}=\hat{G}+20\\\hat{G}=\hat{I}+8\\\hat{G}+\hat{H}+\hat{I}=180\end{cases}

    Using the first two equations, we can express \hat{H} and \hat{I} in terms of \hat{G}:

    \hat{H}=\hat{G}+20,\quad \hat{I}=\hat{G}-8

    So, the last equation becomes

    \hat{G}+(\hat{G}+20)+(\hat{G}-8)=180 \iff 3\hat{G}+12=180 \iff 3\hat{G}=168 \iff \hat{G}=56

    And we deduce

    \hat{H}=\hat{G}+20=76,\quad \hat{I}=\hat{G}-8=48

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