Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

What is the value of x?

"A triangle is shown with two sides that each measure 21. The angle between the two sides is 38 degrees. One of the other base angles is labeled x degrees."

Since the triangle has two equal sides, it is an isosceles triangle, therefore it will also have equal angles.

Since one of the angles is X, the other two angles will be 2X
2X + 38° = 180° ( sum of interior angles in a triangle)
2X = 180° - 38°
2X =142°
To get x we need to find the representing figure, we simply divide both sides by 2
2X/2 = 142/2
X = 71°

Looks like you have an isosceles triangle

so the two base angles must be x each, and
2x + 38 = 180

solve for x

btw, the fact that the sides are 21 is merely a distraction, the fact that
they were both 21 simply told us we had an isosceles triangle, and the
angle property was the key issue

two equal sides ... isosceles triangle ... base angles are equal

2 x = 180º - 38º

Well, well, well, we have a triangle trying to trick us, eh? Let's uncover the value of x step by step!

We have a triangle with two sides measuring 21 units each. The angle between these two sides is 38 degrees. And one of the other base angles is labeled x degrees.

Now, let's remember that the sum of the interior angles of a triangle is always 180 degrees. So, we can use this information to find the value of x.

We know that one of the angles is 38 degrees, and the other base angle is x degrees. So, let's add them up and set the sum equal to 180 degrees:

38 degrees + x degrees = 180 degrees

To get the value of x, we need to isolate it on one side of the equation. Let's subtract 38 degrees from both sides:

x degrees = 180 degrees - 38 degrees

Now, it's time for some subtraction:

x degrees = 142 degrees

Voila! The value of x is 142 degrees. But don't let that triangle fool you again! Make sure you always check your work.

To find the value of x, we can apply the angle sum property of triangles, which states that the sum of the interior angles of a triangle is always 180 degrees.

In this given triangle, we know that the angle between the two sides measures 38 degrees. Since the other two angles are base angles, they must be congruent to each other.

Let's denote the measure of one of the base angles as x degrees. Therefore, the other base angle will also be x degrees.

Now, let's calculate the sum of the interior angles of the triangle:

Sum of interior angles = Angle 1 + Angle 2 + Angle 3 = x + x + 38

According to the angle sum property, this sum should be equal to 180 degrees:

x + x + 38 = 180

Combining like terms:

2x + 38 = 180

Next, we need to isolate the variable x. We can do this by subtracting 38 from both sides of the equation:

2x + 38 - 38 = 180 - 38

Simplifying:

2x = 142

Finally, to find the value of x, we divide both sides of the equation by 2:

2x/2 = 142/2

Simplifying:

x = 71

Therefore, the value of x is 71 degrees.