Math Snap

STEP 1

What is this asking?
We need to find the value of an angle inside a right triangle, given an exterior angle.
Watch out!
Don't forget that a right angle measures $90^\circ$!

STEP 2

1. Find the adjacent angle
2. Find $x$

STEP 3

A straight line forms an angle of $180^\circ$.
The exterior angle of $124^\circ$ and the adjacent angle inside the triangle must add up to $180^\circ$.

STEP 4

Let's call the adjacent angle $a$.
We know that $a + 124^\circ = 180^\circ$.
To find $a$, we subtract $124^\circ$ from both sides:
$$a = 180^\circ - 124^\circ = \mathbf{56^\circ}$$ So, the adjacent angle is $\mathbf{56^\circ}$.

STEP 5

The sum of the angles in any triangle is $180^\circ$.
We have a right triangle, so one angle is $90^\circ$, another is $\mathbf{56^\circ}$ (from the previous step), and the last angle is $x$.

STEP 6

We know that $90^\circ + 56^\circ + x = 180^\circ$.
First, let's combine the known angles:
$$146^\circ + x = 180^\circ$$ Now, we subtract $146^\circ$ from both sides of the equation:
$$x = 180^\circ - 146^\circ = \mathbf{34^\circ}$$ So, $x = \mathbf{34^\circ}$!

The value of $x$ is $\mathbf{34^\circ}$.