Question

Given kite RGBY with RG=RY. If m∠RGB=92 ∘

and m∠YBG=70 ∘ , find m∠GRB.
m∠GRB=99 ∘m∠GRB=53 ∘ m∠GRB=106 ∘
m∠GRB=64 ∘
m∠GRB=128
∘None of the above

Answer 1

To find the missing angle m∠GRB in the kite RGBY, subtract the known angles from the sum of the angles in a kite, which is always 360°.

Step-by-step explanation:

Let's solve for the missing angle, m∠GRB.

Given that kite RGBY has RG = RY, which means that it is an isosceles kite, we know that the angles ∠RGB and ∠YBG are congruent. Therefore, if m∠RGB = 92°, we can say that m∠YBG = 92° as well.

Now, since the sum of the angles in a kite is always 360°, we can find m∠GRB by subtracting the known angles from 360°:

m∠GRB = 360° - m∠RGB - m∠YBG

m∠GRB = 360° - 92° - 92°

m∠GRB = 176°

Therefore, m∠GRB = 176°.