Question

find the measures of the numbered angles in the kite shown to the right.

Explanation:

Step1: Find angle 1

Angle 1 is a right angle.
$\angle1 = 90^\circ$

Step2: Find angle 2

Angle 2 is a right angle.
$\angle2 = 90^\circ$

Step3: Find angle 6

In the left triangle, sum of angles is $180^\circ$.
$\angle6 = 180^\circ - 90^\circ - 29^\circ = 61^\circ$

Step4: Find angle 5

In the right triangle, sum of angles is $180^\circ$.
$\angle5 = 180^\circ - 90^\circ - 51^\circ = 39^\circ$

Step5: Find angle 7

Angle 7 equals angle 6 (congruent triangles).
$\angle7 = 61^\circ$

Step6: Find angle 8

Angle 8 equals angle 5 (congruent triangles).
$\angle8 = 39^\circ$

Step7: Find angle 9

Angle 9 equals the given $29^\circ$ (congruent triangles).
$\angle9 = 29^\circ$

Step8: Find angle 10

Angle 10 equals the given $51^\circ$ (congruent triangles).
$\angle10 = 51^\circ$

Step9: Find angle 3

Angle 3 is a right angle.
$\angle3 = 90^\circ$

Step10: Find angle 4

Angle 4 is a right angle.
$\angle4 = 90^\circ$

Answer:

$\angle1=90^\circ$, $\angle2=90^\circ$, $\angle3=90^\circ$, $\angle4=90^\circ$, $\angle5=39^\circ$, $\angle6=61^\circ$, $\angle7=61^\circ$, $\angle8=39^\circ$, $\angle9=29^\circ$, $\angle10=51^\circ$