In the figure, point B lies on AD. What is the value of 3x?

Explanation

Choice C is correct. Since point B lies on AD, angles ABC and CBD are supplementary. It's given that angle ABC is a right angle; therefore, its measure is 90°. It follows that the measure of angle CBD is 180° − 90°, or 90°. By the angle addition postulate, the measure of angle CBD is equivalent to x ° + 2x ° + 2x °. Therefore, 90 = x + 2x + 2x. Combining like terms gives 90 = 5x. Dividing both sides of this equation by 5 yields x = 18. Therefore, the value of 3x is 3(18), or 54.