Question

How to do this question plz answer my question step by step plzz plz plz plz ​

Answer 1

40°, 95°, 105°, and 160°

Explanation:

Let the smallest angle be x.

Measures of the 3 angles can be expressed as:

`x + 55`

`x + 65`

`x + 120`

The sum of all angles in a quadrilateral = 360°.

Therefore,
`(x + 55) + (x + 65) + (x + 120) = 360`

Solve for x

`x + 55 + x + 65 + x + 120 = 360`

`3x + 240 = 360`

`3x + 240 - 240 = 360 - 240`

`3x = 120`

`(3x)/(3) = (120)/(3)`

`x = 40`

The smallest angle = 40°

Plug in the value of x in the earlier stated expressions to find the measure of the other angles:

`x + 55 = 40 + 55 = 95`

`x + 65 = 40 + 65 = 105`

`x + 120 = 40 + 120 = 160`