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In the figure above, point B lies on bar...


In the figure above, point B lies on `bar(AD)` . What is the value of 3x ?

A

18

B

36

C

54

D

72

Text Solution

Verified by Experts

The correct Answer is:
C
Since point B lies on `bar(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 1`80^@` − `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.
Choice A is incorrect. This is the value of x. Choice B is incorrect. This is the value of 2x. Choice D is incorrect. This is the value of 4x.
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