Question

solve for x. justify your answer with a reason/theorem.
85.
triangle with one angle 80°, another angle x°, and an exterior angle (3x - 22)°
x =
reason:

Explanation:

Step1: Apply exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$3x - 22 = 80 + x$$

Step2: Isolate x terms

Subtract $x$ from both sides:
$$3x - x - 22 = 80$$
$$2x - 22 = 80$$

Step3: Solve for x

Add 22 to both sides, then divide by 2:
$$2x = 80 + 22$$
$$2x = 102$$
$$x = \frac{102}{2} = 51$$

Answer:

$x = 51$
Reason: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles (Exterior Angle Theorem).