In a triangle HJK, HJ = HK. G is a point on HJ such that HG = GK = JK. What is the degree measure of two-third of (∠HGK + ∠GKJ)?

Correct option is A

Given:

​$$\triangle HJK$$​ with HJ = HK

G is a point on HJ such that HG = GK = JK

To Find:

The degree measure of two-third of (∠HGK + ∠GKJ)

Solution:

In $$\triangle HJK$$,

​$$\angle$$JHK + ​$$\angle$$HKJ + ​$$\angle$$HJK = 180$$\degree$$​
x + 2x + 2x = 180$$\degree$$​​

5x = 180$$\degree$$
x = 36$$\degree$$

∠HGK = 180$$\degree - 72\degree =108 \degree$$​​

Now,

$$\frac 23$$​ (∠HGK + ∠GKJ) = $$\frac 23 ( 108\degree + 36\degree)= 96 \degree$$​