Math / Geometry

Question(A)

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ in a right triangle where the other two angles are $x^\circ$ and $2x^\circ$ . Watch out! Don't forget that the angles in a triangle always add up to $180^\circ$ !

STEP 2

1. Set up the equation
2. Solve for x

STEP 3

Alright, so we've got a right triangle, which means one of the angles is $\boldsymbol{90^\circ}$ !
We also know the other two angles are $x^\circ$ and $2x^\circ$ .

STEP 4

The sum of angles in any triangle is always $\boldsymbol{180^\circ}$ .
This is a fundamental fact in geometry!
So, we can set up an equation: $x + 2x + 90 = 180$ .
See how we just added up all three angles and set them equal to $180$ ?

STEP 5

Let's simplify the left side of our equation: $x + 2x$ gives us $3x$ .
So, our equation becomes $3x + 90 = 180$ .

STEP 6

Now, we want to isolate $\boldsymbol{x}$ .
Let's subtract $90$ from both sides of the equation: $3x + 90 - 90 = 180 - 90$ .
This simplifies to $3x = 90$ .
We're getting closer!

STEP 7

Finally, we divide both sides by $3$ to get $x$ all by itself: $\frac{3x}{3} = \frac{90}{3}$ .
This gives us our final answer: $x = 30$ .
Boom!

STEP 8

The value of $x$ is $\boldsymbol{30}$ .
So, the angles in our triangle are $30^\circ$ , $2 \cdot 30^\circ = 60^\circ$ , and $90^\circ$ .

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