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Answer/Step-by-step explanation:
Question 1:
Interior angles of quadrilateral ABCD are given as: m<ABC = 4x, m<BCD = 3x, m<CDA = 2x, m<DAB = 3x.
Since sum of the interior angles = (n - 2)180, therefore:
n = 4, i.e. number of sides/interior angles.
Equation for finding x would be:
(dividing each side by 12)
Find the measures of the 4 interior angles by substituting the value of x = 30:
m<ABC = 4x
m<ABC = 4*30 = 120°
m<BCD = 3x
m<BCD = 3*30 = 90°
m<CDA = 2x
m<CDA = 2*30 = 60°
m<DAB = 3x
m<DAB = 3*30 = 90°
Question 2:
<CDA and <ADE are supplementary (angles on a straight line).
The sum of m<CDA and m<ADE equal 180°. To find m<ADE, subtract m<CDA from 180°.
m<ADE = 180° - m<CDA
m<ADE = 180° - 60° = 120°