Answer/Step-by-step explanation:
1. Given:
m<ABC = 4x°,
m<BCD = 3x°,
m<CDA = 2x°,
m<DAB = 3x°
Sum of quadrilateral = (n - 2)180
Quadrilateral has 4 sides, therefore, n = 4.
Sum of quadrilateral = (4 - 2)180 = 2*180 = 360°
Equation to solve for x would be:
m<ABC + m<BCD + m<CDA + m<DAB = 360
Substituting the given expression for each angle, we have:
4x + 3x + 2x + 3x = 360
12x = 360
Use the above equation to solve for x by dividing both sides by 12
x = 30
Find the measures of all the interior angles by substituting the value of x in each given expression for each angle as follows:
m<ABC = 4x = 4*30 = 120°
m<BCD = 3x = 3*30 = 90°
m<CDA = 2x = 2*30 = 60°
m<DAB = 3x = 3*30 = 90°
[Check: 120 + 90 + 60 + 90 = 360°]
2. <CDA and <ADE form a linear pair. They are supplementary angles.
Since supplementary angles sum up to equal 180°, and <ADE is a supplement of <CDA (60°), therefore:
m<ADE = 180° - 60° = 120°
