Final answer:
To solve for x, the algebraic expressions representing the angles are summed up and set equal to 90 degrees, resulting in x being 8.75. Hence, the correct answer is option (a) 8.75.
Step-by-step explanation:
The student is asking for help in solving a problem involving complementary angles and algebraic expressions. Given that ABD and BDE are complementary angles, the sum of the angles should equal 90 degrees. We’re told that ABD is 3x - 2 degrees and BDE is 5x + 22 degrees. To find the value of x, we need to set up the equation:
3x - 2 + 5x + 22 = 90
This simplifies to:
8x + 20 = 90,
which further simplifies to:
8x = 70.
Now we divide both sides by 8 to get:
x = 8.75.
Therefore, the correct answer is option (a) 8.75.