Math Snap

STEP 1

What is this asking?
We need to find the value of $x$ using the right triangle, and then use that value to find the biggest angle in the other triangle.
Watch out!
Don't forget that angles in a right triangle add up to $90^\circ$ and angles in any triangle add up to $180^\circ$!

STEP 2

1. Solve for x
2. Find the largest angle

STEP 3

Alright, so we've got this right triangle, and we know two of its angles: $(15x)^\circ$ and $(8x - 2)^\circ$.
Since it's a right triangle, the third angle is $90^\circ$!

STEP 4

Now, here's the magic: all the angles in a triangle always add up to $180^\circ$.
So, let's write that down as an equation:
$$(15x) + (8x - 2) + 90 = 180$$

STEP 5

Time to combine like terms!
We've got $15x$ and $8x$, which add up to $23x$.
And we've got $-2$ and $90$, which make $88$.
So, our equation becomes:
$$23x + 88 = 180$$

STEP 6

To isolate our $x$ term, let's subtract $88$ from both sides of the equation:
$$23x + 88 - 88 = 180 - 88$$ $$23x = 92$$

STEP 7

Almost there!
Now, we divide both sides by $23$ to find the value of $x$:
$$\frac{23x}{23} = \frac{92}{23}$$ $$x = 4$$Woohoo! We found that $x = 4$!

STEP 8

Okay, so we know $x = 4$, and we need to find the largest angle in the other triangle.
Its angles are $(24x)^\circ$, $(21x)^\circ$, and $(15x)^\circ$.

STEP 9

Let's substitute $x = 4$ into each angle:
$$24 \cdot 4 = 96$$ $$21 \cdot 4 = 84$$$$15 \cdot 4 = 60$$So, the angles are $96^\circ$, $84^\circ$, and $60^\circ$.

STEP 10

The largest angle is clearly $96^\circ$!

The value of $x$ is $4$, and the largest angle in the second triangle is $96^\circ$.