Question

find the measure of n: 117° 3n° 39 117 25 63

Explanation:

Step1: Recall polygon - angle sum

The sum of interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up the equation

Let the other two non - given angles be equal (since the trapezoid is isosceles as indicated by the congruence marks). Let the sum of the known angles be $117^{\circ}+117^{\circ}+3n^{\circ}+3n^{\circ}=360^{\circ}$. Simplify to $234^{\circ}+6n^{\circ}=360^{\circ}$.

Step3: Solve for n

Subtract $234^{\circ}$ from both sides: $6n^{\circ}=360^{\circ}-234^{\circ}=126^{\circ}$. Then divide both sides by 6: $n=\frac{126}{6}=21$. But if we assume the non - congruent angles are considered, and the sum of the two given angles $117^{\circ}+3n^{\circ}$ and the other two equal angles. Since the sum of interior angles of a quadrilateral is $360^{\circ}$, and assuming the other two equal angles sum to $x + x=2x$. We have $117^{\circ}+3n^{\circ}+2x = 360^{\circ}$. However, if we consider the fact that the trapezoid has two pairs of adjacent angles that are supplementary (in an isosceles trapezoid, base - angles are equal). If we assume the two $117^{\circ}$ angles are base - angles, then the other two angles are equal. Let's use the fact that adjacent angles in a trapezoid are supplementary. The angle adjacent to $117^{\circ}$ is $180 - 117=63^{\circ}$. So $3n = 63$.

Step4: Solve for n from $3n = 63$

Divide both sides by 3: $n = 21$. And $3n=63$.

Answer:

21