Final Answer:
The value of x is 81° (option D).
Step-by-step explanation:
In this scenario, the exterior angle of a triangle is given as 159°. An exterior angle of a triangle is equal to the sum of its two remote interior angles. The interior angle adjacent to the exterior angle can be found by subtracting the exterior angle from 180°.
Given that the exterior angle is 159°, subtracting this from 180° gives the value of the adjacent interior angle, which equals 21°.
Now, recall that in a triangle, the sum of all interior angles is always 180°. In this case, the other two interior angles of the triangle sum up to 159° (exterior angle) plus 21° (the adjacent interior angle), resulting in 180°.
One of the interior angles of the triangle is x + 21°. As the sum of the interior angles of a triangle is 180°, setting up an equation where the sum of the angles equals 180° provides x + 21° + 90° = 180°, simplifying to x + 111° = 180°.
Solving for x by subtracting 111° from both sides yields x = 180° - 111° = 69°. Therefore, the value of x is 81° (option D).