In the isosceles triangle KRG, the bisector GM of the angle G is drawn at the base of KG, ∡GMR = 84 °. Determine the angles of this triangle

<RMK = 180 degrees (flat angle)
<RMK = <RMG + <KMG
<KMG = <RMK- <RMG
<KMG = 180-84 = 96 degrees
<G = <K (base angles are equal)
<RGM = <MGK (MG bisects <G in half)
Let x degrees be <G, then 2x – <K
x + 2x + 96 = 180 (the sum of the angles in the triangle is 180 degrees)
3x + 96 = 180
3x = 180-96
3x = 84
x = 84: 3
x = 28
28 degrees – <G
<K = 28 * 2 = 56
<G + <K + <R = 180 degrees (the sum of the angles in a triangle is 180 degrees)
<R = 180 – (<G + <K)
<R = 180- (28 + 56) = 96 degrees
Answer: <G = 28 degrees; <K = 56 degrees; <R = 96 degrees