Final answer:
To find the measure of angle YBR in the kite RGBY, given that BG equals BY and that m∠RGB is 92 degrees and m∠YRG is 80 degrees, subtract the known angles from 360 degrees.
The calculation shows that m∠YBR is 96 degrees.
Step-by-step explanation:
The problem involves finding the measure of an angle in a kite, given the measures of other angles. The kite RGBY has equal sides BG and BY, and the measures of angles RGB and YRG are provided. To find the measure of angle YBR, we need to use the properties of kites and the knowledge that the sum of angles around a point is 360 degrees.
Firstly, kites have two pairs of adjacent sides that are equal in length. Since BG equals BY, angle G and angle Y must be equal because they are opposite the equal sides. Secondly, the sum of the interior angles in any quadrilateral is 360 degrees. Thus, we can find the measure of angle YBR by subtracting the known angle measurements from 360 degrees.
Given that m∠RGB is 92 degrees and m∠YRG is 80 degrees, the sum of angles RGB and YRG is 172 degrees. Since angle G and angle Y are equal, angle G is also 92 degrees. Subtracting these three angles from 360 degrees gives us the measure of angle YBR:
360 degrees - (92 degrees + 80 degrees + 92 degrees) = 96 degrees.
Therefore, the measure of angle YBR in kite RGBY is 96 degrees.