Question

In the figure below are represented the angles AOB, BOC, COD with measures directly proportional to numbers 2; 3 and 5.Knowing that the semi-lines OA and OD are opposites, the small angle measure is equal to:
a) 18°
b) 90°
c) 36°
d) 144°​​

Answer 1

Answer:

C

Step-by-step explanation:

given the angle in the ratio 2 : 3 : 5 = 2x : 3x : 5x ( x is a multiplier )

∠ AOB , ∠ BOC and ∠ COD lie on a straight line, AD and sum to 180°

sum the angles, equate to 180 and solve for x

2x + 3x + 5x = 180

10x = 180 ( divide both sides by 10 )

x = 18

Then

∠ AOB = 2x = 2 × 18 = 36°

∠ BOC = 3x = 3 × 18 = 54°

∠ COD = 5x = 5 × 18 = 90°

The small angle AOB has a measure of 36°