A triangle has an exterior angle of 110 degrees, what is the value of angle x?
To find the value of angle x in a triangle with an exterior angle of 110 degrees, we can use the fact that the sum of the measures of the interior angles of a triangle is always 180 degrees.
An exterior angle of a triangle is formed by extending one of its sides. Since the exterior angle is 110 degrees, the sum of the exterior angle and the interior angle adjacent to it (angle x) will be 180 degrees.
Therefore, we can write the equation:
x + 110 = 180
To solve for x, we can subtract 110 from both sides of the equation:
x = 180 - 110
x = 70
So, the value of angle x is 70 degrees.
Since the exterior angle of a triangle is equal to the sum of the two opposite interior angles, we can set up the following equation:
x + (x + 110) = 180
Simplifying the equation:
2x + 110 = 180
Subtracting 110 from both sides:
2x = 70
Dividing both sides by 2:
x = 35
Therefore, the value of angle x is 35 degrees.