A side of the triangle below has been extended to form an exterior angle of 121°. Find the value of xx.
121°
x°
To find the value of x, we can use the property that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
Let's call the two opposite interior angles a and b.
The sum of the measures of the exterior angle and the two opposite interior angles is 180° (since the angles in a triangle add up to 180°).
So we can write the following equation:
121° + a + b = 180°
To find the value of x, we need to solve for a or b. Let's choose to solve for a.
First, subtract 121° from both sides of the equation:
a + b = 180° - 121°
a + b = 59°
Now, we can substitute the value of a in terms of x using the given information that x is an interior angle:
a = x°
So we have:
x° + b = 59°
To solve for x, subtract b from both sides of the equation:
x° = 59° - b
Therefore, the value of x is 59° - b.