A side of the triangle below has been extended to form an exterior angle of 76°. Find the value of x.
Top 51°
We know that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. Let's call the angle adjacent to the extended side as angle A. Therefore, angle A + 51° = 76°.
Subtracting 51° from both sides gives us angle A = 25°.
Since angles in a triangle add up to 180°, the remaining angle opposite to the extended side is 180° - (76° + 25°) = 79°.
Now, we have a triangle with angles 25°, 51°, and 79°. Since the sum of the angles in a triangle is 180°, we can write:
25° + 51° + 79° = 180°
Simplifying the equation gives us:
155° = 180° - x
Rearranging the equation to solve for x gives us:
x = 180° - 155°
x = 25°
Therefore, the value of x is 25°.