The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.
The figure shows a triangle with 2 congruent sides. The angle between the congruent sides measures x degrees and a different angle measures 70 degrees.
Let's call the other angle opposite the congruent side "y".
We know that the sum of the interior angles in a triangle is 180 degrees, so we can set up an equation:
x + y + 70 = 180
We also know that the angles opposite the congruent sides are congruent, so:
x = y
We can substitute y for x in the equation:
y + y + 70 = 180
2y + 70 = 180
Subtract 70 from both sides:
2y = 110
Divide by 2:
y = 55
Since x and y are congruent angles, x must also be 55 degrees.
Therefore, the value of x in the triangle is 55 degrees.
make it shorter so i can put it in my words
1. Let's call the other angle opposite the congruent side "y".
2. We know that x + y + 70 = 180.
3. Since x and y are congruent, we can substitute y for x in the equation.
4. Solving for y, we get y = 55.
5. Therefore, x must also be 55 degrees.
6. The value of x in the triangle is 55 degrees.
To find the value of x, we can use the fact that the angles opposite the congruent sides of an isosceles triangle are congruent.
Let's call the angle opposite the congruent sides y. Since we know that the other angle measures 70 degrees, we can set up the following equation:
y + 70 = 180
To solve for y, we can subtract 70 from both sides:
y = 180 - 70
y = 110
Now, we know that the angle opposite the congruent sides is 110 degrees. Since the triangle is isosceles, the other angle opposite the congruent sides will also measure 110 degrees.
The angle between the congruent sides can be found by subtracting the sum of the two congruent angles from 180 degrees:
x = 180 - (110 + 110)
x = 180 - 220
x = -40
Therefore, the value of x in the triangle is -40 degrees.