Answer:
72°, 108°, 72°, and 108°
Step-by-step explanation:
Theorem: Adjacent angles of a parallelogram are SUPPLEMENTARY
Supplementary means they add up to 180 degrees.
Thus, if one angle is "x", the other is "180 - x"
Since it is given two adjacent angles are in the ratio 2 is to 3, we can write:
[tex]\frac{x}{180-x}=\frac{2}{3}[/tex]
We cross multiply and find x:
[tex]\frac{x}{180-x}=\frac{2}{3}\\3x=2(180-x)\\3x=360-2x\\5x=360\\x=\frac{360}{5}\\x=72[/tex]
Thus, the other is:
180 - 72 = 108
The other angles (3rd and 4th) are same as these two. hence the 4 angles of the parallelogram are:
72°, 108°, 72°, and 108°
