Answer
a. $95$
b. $150$
c. $150$
Work Step by Step
The conjecture we will use is the following:
"The sum of a quadrilateral's angles is $360^\circ$."
a. We solve the equation:
$$\begin{align*}
360& = 100 + 80 + 85 + x\\
360&=265+x\\
x& = 360 - 265\\
x& = 95.\end{align*}$$ b. We solve the equation:
$$\begin{align*}
360& = 78+ 60 + 72 + x\\
360&=210+x\\
x& = 360 - 210\\
x& =150.\end{align*}$$ c. We solve the equation:
$$\begin{align*}
360& = 30 +90 + 90 + x\\
360&=210+x\\
x& = 360 - 210\\
x& = 150.\end{align*}$$
