00:57:49

Time remaining

Lines and Angles

Q#StatusQ1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19

Question 1 of 19

Use the following information to answer the next question.

In the given figure, lines AB and CD intersect at point O.

If x: y = 2:3, then what is the measure of ∠BOD?

A.

36°

B.

72°

C.

108°

D.

120°

Next Question »

Dearsir

can u answer this question

It is given that x: y is 2:3.

Then, let the value of xand y be 2m and 3m respectively.

In the given figure, it can be seen that ∠AOC and ∠COB form a linear pair.

∴∠AOC + ∠COB = 180°

⇒ 2m+ 3m = 180°

⇒ 5m= 180°

⇒ = 36°

∴∠AOC = 2m = 72° and ∠COB = 3m = 108°

In the given figure, ∠COB and ∠BOD form a linear pair.

∴COB + ∠BOD = 180°

⇒ ∠BOD = 180° − ∠COB

⇒ ∠BOD = 180° − 108°

⇒ ∠BOD = 72°

Thus, the measure of ∠BOD is 72°.

Alternate Solution:

∠BOD = ∠AOC [Vertically opposite angles]

∴∠BOD = 72°

The correct answer is B.