Question

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

Explanation:

Step1: Recall kite angle property

In a kite, one pair of opposite angles are equal, and the sum of all interior angles of a quadrilateral is $360^\circ$. The angles between the non-congruent sides are equal, so $b^\circ = 61^\circ$.

Step2: Set up angle sum equation

$$121^\circ + 61^\circ + 61^\circ + a^\circ = 360^\circ$$

Step3: Calculate sum of known angles

$$121 + 61 + 61 = 243$$

Step4: Solve for $a$

$$a = 360 - 243$$

Answer:

$a = 117$