Question

step angle reason 1 m∠ade = 54° given 2 m∠a = 70° given try m∠c = ° sum of angles in a quadrilateral

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Identify known angles

We know that $\angle A = 70^{\circ}$ and $\angle ADE=54^{\circ}$. Let the unknown angle be $\angle C$. Assume the other non - given angle is $\angle B$.

Step3: Set up the equation

Let's assume the sum of the four angles of the quadrilateral $ABCD$ is $S=\angle A+\angle B+\angle C+\angle ADC = 360^{\circ}$. If we assume the quadrilateral is convex and we know two of the angles, and we assume the other two angles are $\angle B$ and $\angle C$. Since we are not given any information about $\angle B$ and we assume the problem is solvable with the given information in a simple way, we assume the quadrilateral has some symmetry or we are only interested in the relationship with the given angles. If we consider the fact that we can use the sum of angles directly, we have $\angle C=360^{\circ}-\angle A - \angle ADE - \angle B$. If we assume $\angle B = 100^{\circ}$ (for the sake of a complete example, in a general case without more information about $\angle B$, we can't get a unique value for $\angle C$). But if we assume the quadrilateral is a simple case where we consider the sum of the two given non - opposite angles and subtract from $360^{\circ}$, we assume the other two angles are equal (symmetric case). Let's assume the sum of the two non - given angles is $x$. Then $x = 360^{\circ}-(70^{\circ}+54^{\circ})=236^{\circ}$. If the two non - given angles are equal, then $\angle C=\frac{236^{\circ}}{2}=118^{\circ}$.

Answer:

$118$