Question

In the given figure, if a:b=10:13, then /_xoy equals.​

Answer 1

Answer:

2x + 7 = 3x - 7

3x - 2x = 7 + 7

x = 14

2x + 7 + 12y + 1 = 180

2(14) + 12y + 8 = 180

28 + 12y + 8 = 180

36 + 12y = 180

12y = 180 - 36 = 144

y = 144/12 = 12

x = 14, y = 12

Answer 2

Answer:

  m∠XOY = 80°

Step-by-step explanation:

We can make use of the fact that an exterior angle of a triangle is equal to the sum of the remote interior angles. The two angles marked with measures are exterior angles, so we can write the relations ...

  132° = O +b

  120° = O +a

Subtracting the second equation from the first, we get ...

  (132°) -(120°) = (O +b) -(O +a)

  12° = b -a

We observe that b:a = 13:10, a difference of 13-10 = 3 ratio units. Then each of those ratio units must stand for 12°/3 = 4°. The values of 'a' and 'b' are then ...

  a : b = 10 : 13 = 40° : 52° . . . . . multiply ratio units by 4°, note b-a = 12°

Using the value for 'a' in the second of the original equations, we find ...

  120° = O +40° . . substitute 40° for 'a'

  80° = O . . . . . . . subtract 40°

The measure of angle XOY is 80°.