Question

Rays BA and BC are perpendicular. Point D lies in the interior of angle ABC. If angle ABD = 3r + 5 and angle DBC = 5r - 27, find the value of r.

A) 4
B) 7
C) 8
D) 10

Answer 1

The value of r is 14.

Step-by-step explanation:

We are given that rays BA and BC are perpendicular, and point D lies in the interior of angle ABC. We are given that angle ABD = 3r + 5 and angle DBC = 5r - 27. Since rays BA and BC are perpendicular, the sum of angle ABD and angle DBC must be 90 degrees. Therefore, we can set up the equation:

3r + 5 + 5r - 27 = 90

Combining like terms, we get:

8r - 22 = 90

Adding 22 to both sides, we get:

8r = 112

Dividing both sides by 8, we get:

r = 14

Therefore, the value of r is 14. So the correct option is D) 10.