Question

How do you solve these two problems please explain step by step

Answer 1

Answer:

1) $x=15, y=41$

2) $x=6, y=24$

Step-by-step explanation:

1)

The two triangles are similar by AA similarity.

That means $5x-5=4x+10$.

We can add $5$ to both sides to get $5x=4x+15$.

We can then subtract $4x$ from both sides to get $x=15$.

We know that the $(5x-5)+(6y-4)=180$  because they both lie on a straight line.

We can plug in for $x$ to get $(5(15)-5)+(6y-4)=75-5+6y-4=6y-66=180$.

We can divide both sides of the equation by $6$ to get $y-11=30$.

We then add $11$ to both sides to get $y=41$.

So, $\boxed{x=15, y=41}$ and we're done!

2)

Because the two bases of a trapezoid are parallel, meaning adjacent top and bottom angles sum to $180^{\circ}$, we have that $90+3y+18=180$.

We can subtract a $90$ and an $18$ from both sides to get $3y=72$.

We then divide both sides of the equation by $3$ to get $y=24$.

We do the same thing for $x$. On the other side of the trapezoid, we have that $15x+30+10x=180$.

We combine like terms on the left side to get $25x+30=180$.

We subtract a $30$ from both sides to get $25x=150$.

We divide both sides of the equation to get $x=6$.

So, $\boxed{x=6, y=24}$ and we're done!