Question8.
Studdy Solution
STEP 1
What is this asking? We're looking for the value of in a triangle where we know all the sides have the same length, and one angle is degrees. Watch out! Don't forget that the angles in *any* triangle add up to 180 degrees!
STEP 2
1. Recognize the triangle type
2. Find the value of
STEP 3
Hey everyone!
Look at this triangle!
Notice anything special about the sides?
They're all the same length, \(5\)!
That means it's an **equilateral triangle**!
And guess what's cool about equilateral triangles?
All their angles are also the same!
STEP 4
So, if all the angles are equal, and we know that one angle is \(3x degrees, we can write an equation!
Since the angles in *any* triangle add up to \(180 degrees, and all three angles in *this* triangle are equal to \(3x, we have \(3x + 3x + 3x = 180\).
STEP 5
Let's simplify that!
We have \(3 lots of \(3x\) on the left side, which is \(9x\).
So, our equation becomes \(9x = 180\).
STEP 6
Now, to get the value of \(x\), we need to get it all by itself.
Since \(x is being multiplied by \(9\), we'll **divide both sides** of the equation by \(9\).
This gives us \( \frac{9x}{9} = \frac{180}{9} \).
STEP 7
On the left side, the \(9s divide to one, leaving us with just \(x\).
On the right side, \(180 divided by \(9 is \(20\).
So, we have \(x = 20\)!
STEP 8
We found that \(x = 20\)!
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