Answer: x = 81 / 18
Explanation:
To find the value of x such that ∠BGD is a right angle, we need to set up an equation using the given angle measurements.
In a right angle, the sum of the two adjacent angles is 90 degrees. Therefore, we can write the equation:
∠BGC + ∠CGD = 90
Substituting the given angle measurements:
(16x - 4) + (2x + 13) = 90
Now, let's solve this equation for x:
16x - 4 + 2x + 13 = 90
18x + 9 = 90
18x = 90 - 9
18x = 81
x = 81 / 18