in the figure below, what are the values of x and y? What are the measures of the four angles in the figure

a. x=57.6, y=44.8

Step-by-step explanation:

Named the angles, check the picture for that

<ABD+<ACD=180 (Opposite angles of a quadrilateral is supplementary (180 degrees)

<CAB+<BDC=180 (Opposite angles of a quadrilateral is supplementary (180 degrees)

therefore:

a. 3y+x-12=180.............. equ 1

2x+y+20=180.............equ 2

From equ 1

x+3y=180+12

x+3y=192...............equ 3

From equ 2

2x+y=180-20

2x+y=160.............equ 4

Equate equ 3 and equ 4

x+3y=192...............equ 3

2x+y=160.............equ 4

Using elimation method

x+3y=192...............equ 3

2x+y=160.............equ 4

Multiple equ 3 by 1 and equ 4 by 3

x+3y=192...............equ 3 ×1

2x+y=160.............equ 4 ×3

x+3y=192

6x+3y=480

Subtract

-5x+0=-288

-5x=-288

x=57.6................... Equ 5

Replace 57.6 for x in equ 3

x+3y=192...............equ 3

57.6+3y=192

3y=192-57.6

3y=134.4

y=44.8

B. <CAB= 2x=2×57.6=115.2

<ABD= 3y=3×44.8= 134.4

<ACD=x-12=57.6-12=45.6

<BDC=y+20=44.8+20=64.8

answer is 144

step-by-step explanation: