Question

in convex pentagon abcde, segment ab is parallel to segment de. the measure of angle b is 139 degrees, and the measure of angle d is 174 degrees. what is the measure, in degrees, of angle c?

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. For a pentagon, $n = 5$, so the sum of the interior angles is $(5 - 2)\times180^{\circ}=540^{\circ}$.

Step2: Use the property of parallel lines

Since $AB\parallel DE$, we can consider the angles formed. But we can also directly use the sum of angles formula. Let $\angle A=x$, $\angle B = 139^{\circ}$, $\angle C=y$, $\angle D=174^{\circ}$, $\angle E = z$.
We know that $x + y+z + 139^{\circ}+174^{\circ}=540^{\circ}$.
We don't need to find $\angle A$ and $\angle E$ separately. We can just solve for $y$.

Step3: Solve for $\angle C$

$y=540^{\circ}-(139^{\circ}+174^{\circ})$
$y = 540^{\circ}-313^{\circ}$
$y = 227^{\circ}$

Answer:

$227$