The problem asks to find the measure of angle D in a kite ABCD, where angle A is $36^{\circ}$ and angle C is $70^{\circ}$.

1. Problem Description

The problem asks to find the measure of angle D in a kite ABCD, where angle A is $36^{\circ}$ and angle C is $70^{\circ}$.

2. Solution Steps

A kite is a quadrilateral. The sum of the interior angles of any quadrilateral is $360^{\circ}$. In a kite, one diagonal is the perpendicular bisector of the other. Also, a kite has two pairs of adjacent sides that are congruent. Moreover, the angles between non-congruent sides are congruent. In kite ABCD, since AB = BC, and AD = CD, we have $\angle D = \angle B$.

We know that the sum of the interior angles of a quadrilateral is $360^{\circ}$. Thus,

$\angle A + \angle B + \angle C + \angle D = 360^{\circ}$.

Given that $\angle A = 36^{\circ}$ and $\angle C = 70^{\circ}$, and also $\angle B = \angle D$, we can substitute these values into the equation:

$36^{\circ} + \angle B + 70^{\circ} + \angle D = 360^{\circ}$.

Since $\angle B = \angle D$, let $\angle B = \angle D = x$.

$36^{\circ} + x + 70^{\circ} + x = 360^{\circ}$.

$2x + 106^{\circ} = 360^{\circ}$.

$2x = 360^{\circ} - 106^{\circ}$.

$2x = 254^{\circ}$.

$x = \frac{254^{\circ}}{2}$.

$x = 127^{\circ}$.

Therefore, $\angle D = 127^{\circ}$.

3. Final Answer

$m\angle D = 127^{\circ}$