Fine the values of x and y on geometry

Y=51, X=23

Step-by-step explanation:

First find y, all angles of a triangle will add up to 180, so set it up as 39+y+90=180

add like terms 39 and 90 to get 129, y+129=180

subtract 129 from 180 to get 51, y=51

Next find x, first you must find the bottom right angle of x's triangle, since a straight line is 180, you must add the three angles that form a straight line to get 180

set it up as 50+y+z=180 (z is our unlabeled angle in the bottom right of x's triangle, we know y=51 so fill that in

50+51+z=180, add 50 and 51 and subtract from 180 to get 101

101 is our z that we need to use to find x

Last equation, 101+56+x=180, solve for x, x=23

let's fu(!

step-by-step explanation:

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9