Answer:1
1. [tex]x = 30[/tex]
2. ∠ABC = 120°, ∠BCD = 90°, ∠CDA = 60°, ∠DAB = 90°
Step-by-step explanation:
It's important to note here that the measure of all interior angles in a quadrilateral will add up to 360°
We know this using the formula[tex](n-2)\cdot 180[/tex], a 4 sided figures angles will add up to
[tex](4-2)\cdot 180\\\\2\cdot 180\\\\360[/tex]
This means that all of the angles (4x, 3x, 2x, 3x) will add up to 360.
[tex]4x + 3x + 2x + 3x = 360[/tex]
Combine like terms:
[tex]12x = 360[/tex]
Divide both sides by 12:
[tex]x = 30[/tex]
We know now substitute x for 30 in for all of the side lengths.
∠ABC = 4x = [tex]4\cdot 30 = 120[/tex]°
∠BCD = 3x = [tex]3\cdot 30 = 90[/tex]°
∠CDA = 2x = [tex]2\cdot 30 = 60[/tex]°
∠DAB = 3x = [tex]3\cdot 30 = 90[/tex]°
Hope this helped!
