Question

question 11
6.67 pts
in kite abcd below, ab = ad, cb = cd, ∠a has a measure of 91°, and ∠b has a measure of 93°.
what is the measure of ∠c?
○ 83°
○ 91°
○ 88°
○ 85°

Explanation:

Step1: Sum of quadrilateral angles

A quadrilateral's total angles = $360^\circ$.

Step2: Kite angle property

Kite has two pairs of equal adjacent angles: $\angle A=\angle C$? No, wait—wait, the kite here has $AB=AD$ (so $\angle ABD=\angle ADB$) and $CB=CD$ (so $\angle CBD=\angle CDB$). Wait, no, better: total angles sum to 360. Given $\angle A=91^\circ$, $\angle B=93^\circ$, and $\angle D=\angle B=93^\circ$ (since $AB=AD$ and $CB=CD$, adjacent angles at B and D are equal). So $\angle C=360-(91+93+93)$.

Step3: Calculate $\angle C$

$\angle C=360 - 277 = 83^\circ$.

Answer:

A. 83°