Question

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

Answer 1

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

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