Question

1. your friend tries to solve $m\angle h$. your friend did not set up to solve for $m\angle h$ correctly. explain

to your friend their misunderstanding and how to set it up correctly.
your friends work
$m\angle h=m\angle l$
$9y + 17 = 10y$
explain to your friend their misunderstanding and
how to set it up correctly.

Explanation:

Step1: Analyze the equation setup

Your friend set \(m\angle H = m\angle L\). But if \(\angle H\) and \(\angle L\) are not congruent (assuming from the problem context of a misunderstanding), this is incorrect. The correct relationship might be based on some geometric property like supplementary angles (if they are adjacent and form a linear - pair) or some other angle - relationship in a geometric figure (e.g., triangle, parallelogram etc.). For example, if \(\angle H\) and \(\angle L\) are supplementary (sum to \(180^{\circ}\)), the equation should be \(m\angle H+m\angle L = 180^{\circ}\). If we assume a different relationship, say \(\angle H\) is part of a triangle and \(\angle L\) is an exterior angle, there are different angle - sum rules. But based on the given \(9y + 17=10y\) (derived from \(m\angle H=m\angle L\) where \(m\angle H = 9y + 17\) and \(m\angle L=10y\)), the misunderstanding is that the friend assumed the two angles are equal.

Step2: Correct equation setup

If, for example, \(\angle H\) and \(\angle L\) are supplementary (a common non - congruent angle relationship), then \(m\angle H+m\angle L=180^{\circ}\). Substituting \(m\angle H = 9y + 17\) and \(m\angle L = 10y\), we get the equation \((9y + 17)+10y=180\).

Step3: Solve the correct equation

First, combine like terms: \(9y+10y+17 = 180\), which simplifies to \(19y+17 = 180\). Then subtract 17 from both sides: \(19y=180 - 17=163\). Finally, divide both sides by 19: \(y=\frac{163}{19}\approx8.58\).

Answer:

The friend's misunderstanding was assuming \(m\angle H = m\angle L\). If, for example, \(\angle H\) and \(\angle L\) are supplementary, the correct equation is \((9y + 17)+10y = 180\). Solving this:

• Combine like terms: \(19y+17 = 180\)
• Subtract 17: \(19y=163\)
• Divide by 19: \(y = \frac{163}{19}\)