Question

find the measures of the following angles in the kite shown below.
note: figure may not be drawn to scale.
a =
b =

Explanation:

Step1: Find angle a

In a kite, the diagonal between the vertices of the non-congruent angles bisects those angles, and the triangles formed are right triangles? No, first, use triangle angle sum. The triangle with 35°: the two adjacent sides are congruent, so it's isosceles. The angle at the top: $180^\circ - 2\times35^\circ = 110^\circ$. Wait, no, the diagonal splits the kite into two congruent triangles? No, the diagonal connecting the vertices of the congruent sides: actually, the angle $a$ is in a right triangle? No, the diagonals of a kite are perpendicular, so $c=90^\circ$. Then, in the triangle with $a^\circ$, $35^\circ$, and $90^\circ$: $a = 180^\circ - 90^\circ - 35^\circ = 55^\circ$.
$a = 180 - 90 - 35 = 55$

Step2: Find angle b

Similarly, in the right triangle with $24^\circ$, $b^\circ$, and $90^\circ$: $b = 180^\circ - 90^\circ - 24^\circ = 66^\circ$.
$b = 180 - 90 - 24 = 66$

Step3: Find angle c

Diagonals of a kite are perpendicular, so $c=90^\circ$.
$c = 90$

Step4: Find angle d

The triangle with $d^\circ$ is congruent to the triangle with $a^\circ$ (since the kite has two pairs of adjacent congruent sides), so $d = a = 55^\circ$.
$d = 55$

Answer:

$a = 55$, $b = 66$, $c = 90$, $d = 55$