find the measures of the interior angles.. (triangle)
110-x , 3x-10, 2x
write equation too .
To find the measures of the interior angles of a triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's write the equation using the given measures:
(110 - x) + (3x - 10) + (2x) = 180
Now, let's solve the equation step-by-step:
110 - x + 3x - 10 + 2x = 180 (removing parentheses)
110 + 2x - 10 + 2x = 180 (combining like terms)
4x + 100 = 180 (combining like terms)
Next, let's isolate the variable by subtracting 100 from both sides:
4x = 180 - 100 (subtracting)
4x = 80 (simplifying)
Finally, let's solve for x by dividing both sides by 4:
x = 80 / 4 (dividing)
x = 20 (simplifying)
Now that we have found the value of x, we can substitute it back into the measures of the interior angles to find their values:
Angle 1 = 110 - x = 110 - 20 = 90 degrees
Angle 2 = 3x - 10 = 3(20) - 10 = 50 degrees
Angle 3 = 2x = 2(20) = 40 degrees
So, the measures of the interior angles are: 90 degrees, 50 degrees, and 40 degrees.
To find the measures of the interior angles of a triangle, we can use the fact that the sum of the interior angles is always 180 degrees.
Let's denote the measures of the interior angles as follows:
Angle 1 = 110 - x
Angle 2 = 3x - 10
Angle 3 = 2x
According to the sum of the interior angles in a triangle, we can write the equation:
Angle 1 + Angle 2 + Angle 3 = 180
Plug in the values:
(110 - x) + (3x - 10) + (2x) = 180
Now, let's solve this equation to find the value of x, and then we can substitute it back into the expressions for the angles to get their measures.
The angles of a triangle always sum to 180°
So:
110° - x + 3x - 10° + 2x = 180°
-x + 3x + 2x = 180° - 110° + 10°
4x = 80° Divide both sides with 4
x = 20°
First angle = 110° - 20° = 90°
Second angle =3 20° - 10° = 60° - 10° = 50°
Third angle = 2 20° = 40°