Question

Given kite RGBY with RG=RY. If m∠RGB=92° and m∠YBG=70°, find m∠GRB.

a) m∠GRB=99°
b) m∠GRB=70°
c) m∠GRB=92°
d) (m\angle GRB = 80^\circ)

Answer 1

To find m∠GRB in the given kite RGBY with RG=RY, we can use the properties of kites and the sum of angles in a kite. By substituting the given values and solving the equation, we find that m∠GRB is equal to 106°.

Step-by-step explanation:

Given kite RGBY with RG=RY, we can determine m∠GRB using the properties of kites.

Since RG=RY, we know that ∠YRG=∠GRY. And since the sum of the angles in a kite is 360°, we can write the equation:

m∠RGB + m∠YRG + m∠GRY + m∠YBG = 360°

Substituting the given values, we get:

92° + ∠GRY + ∠YGR + 70° = 360°

Simplifying the equation gives:

∠GRY + ∠YGR = 198°

Since ∠GRY=∠YRG, we can rewrite the equation as:

∠GRB + ∠GRY = 198°

Finally, substituting the known values:

∠GRB + 92° = 198°

Solving for ∠GRB gives:

∠GRB = 198° - 92°∠GRB = 106°

Therefore, the answer is m∠GRB=106°.