Question

Please help! ^^ thank you!

Answer 1

Solving for x and y given the angles that are in terms of x and y

Answer:

$x = 16$ and $y = 20$

Step-by-step explanation:

Angles $(5x -16)^{\circ}$ and $(6y -4)^{\circ}$ are supplementary. this means they should add up to $180^{\circ}$. we can write the equation: $(5x -16)^{\circ} +(6y -4)^{\circ} = 180^{\circ}$

Also, we can see that angles $(6y -4)^{\circ}$ and $(7x +4)^{\circ}$ are transversals. Transversal angles are equal. we can therefore write the equation: $(6y -4)^{\circ} = (7x +4)^{\circ}$.

We now have the system of equations:

$\begin{cases} (5x -16)^{\circ} +(6y -4)^{\circ} = 180^{\circ} \\ (6y -4)^{\circ} = (7x +4)^{\circ} \end{cases}$

Let's solve for $y$ in terms of $x$ in this equation, $(6y -4)^{\circ} = (7x +4)^{\circ}$, first.

$(6y -4)^{\circ} = (7x +4)^{\circ} \\ 6y -4 = 7x +4 \\ 6y = 7x +4 +4 \\ 6y = 7x +8 \\ y = \frac{7x +8}{6}$

Now let's solve for the equation $(5x -16)^{\circ} +(6y -4)^{\circ} = 180^{\circ}$ by plugging in $y$.

$(5x -16)^{\circ} +(6y -4)^{\circ} = 180^{\circ} \\ 5x -16 +6y -4 = 180 \\ 5x +6y -20 = 180 \\ 5x +6(\frac{7x +8}{6}) -20 = 180 \\ 5x +7x +8 -20 = 180 \\ 12x -12 = 180 \\ 12x = 180 +12 \\ 12x = 192 \\ x = \frac{192}{12} \\ x = 16$.

Now let's just solve for the equation, $y = \frac{7x +8}{6}$, by plugging in the value of $x$.

$y = \frac{7(16) +8}{6} \\ y = \frac{112 +8}{6} \\ y = \frac{120}{6} \\ y = 20$