Question

determine the unknown variables in each figure below. treat each figure as a separate problem.
a)
b)
c)
( d = )
( f = )
( g = )
( h = mathrm { cm } )
( j = mathrm { cm } )

Explanation:

Step1: Find \(d\)

Since the figure is a trapezoid with parallel sides, \(d = 180^{\circ}-49^{\circ}\) (supplementary angles).
\(d = 131^{\circ}\)

Step2: Find \(f\)

\(f = 180^{\circ}-d\) (supplementary angles).
\(f = 49^{\circ}\)

Step3: Find \(g\)

\(g = 180^{\circ}-73^{\circ}\) (supplementary angles).
\(g = 107^{\circ}\)

Step4: Find \(h\)

Using the mid - segment formula for a trapezoid \(h=\frac{7 + 14}{2}\) (mid - segment length is the average of the two parallel sides).
\(h=\frac{21}{2}=10.5\)

Step5: Find \(j\)

Using the mid - segment formula \(8.2=\frac{6 + j}{2}\), then \(6 + j=16.4\) (multiply both sides by 2).
\(j=16.4 - 6=10.4\)

Answer:

\(d = 131^{\circ}\), \(f = 49^{\circ}\), \(g = 107^{\circ}\), \(h = 10.5\) cm, \(j = 10.4\) cm