Question

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

Answer 1

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:

$x + 55$

$x + 65$

$x + 120$

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

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

Solve for x

$x + 55 + x + 65 + x + 120 = 360$

$3x + 240 = 360$

$3x + 240 - 240 = 360 - 240$

$3x = 120$

$\frac{3x}{3} = \frac{120}{3}$

$x = 40$

The smallest angle = 40°

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

$x + 55 = 40 + 55 = 95$

$x + 65 = 40 + 65 = 105$

$x + 120 = 40 + 120 = 160$