Answer:
40°, 95°, 105°, and 160°
Step-by-step explanation:
Let the smallest angle be x.
Measures of the 3 angles can be expressed as:
[tex] x + 55 [/tex]
[tex] x + 65 [/tex]
[tex] x + 120 [/tex]
The sum of all angles in a quadrilateral = 360°.
Therefore, [tex] (x + 55) + (x + 65) + (x + 120) = 360 [/tex]
Solve for x
[tex] x + 55 + x + 65 + x + 120 = 360 [/tex]
[tex] 3x + 240 = 360 [/tex]
[tex] 3x + 240 - 240 = 360 - 240 [/tex]
[tex] 3x = 120 [/tex]
[tex] \frac{3x}{3} = \frac{120}{3} [/tex]
[tex] x = 40 [/tex]
The smallest angle = 40°
Plug in the value of x in the earlier stated expressions to find the measure of the other angles:
[tex] x + 55 = 40 + 55 = 95 [/tex]
[tex] x + 65 = 40 + 65 = 105 [/tex]
[tex] x + 120 = 40 + 120 = 160 [/tex]
