Question

in the given figure,AB=AC,CH=CB and HK is congruent to BC if angle CAX =137° then find angle CHK​

Answer 1

Answer:

Given exterior ∠A = 140

Hence, ∠BAC=180−140=40

Since, AB=AC, ∠ABC=∠ACB

In triangle ABC, ∠ABC=2180−40 =70

Since, HK∥BC,

∠AHK=∠AKH=∠ABC=70

∠AKH+∠HKC=180

∠HKC=110

Since, CH=CB

∠BHC=∠ABC=70

∠BHC+∠AHK+∠CHK=180

∠CHK=180−140=40

Now, in triangle CHK

∠CHK+∠HKC+∠HCK=180

∠HCK=180−150=30.