Question

In a fig AB=AC, CH=CB, HK is parallel to BC. if Angle CAX=137 degrees then find Angle CHK

Answer 1

Step-by-step explanation:

Given : AB=AC,CH=CB and HK∥BC

TO FIND: ∠CHK

SINCE AB=AC 

THUS, ΔABC IS ISOSCELES.

∠DAC IS THE EXTERNAL ANGLE, WHICH EQUALS SUM OF OPPOSITE INTERIOR ANGLES:

∠DAC=∠ABC+∠ACB

⇒1370=2∠ABC

[∠ABC=∠ACB]

⇒∠ABC=68.50

SINCE HK∥BC,∠KHB+∠HBC=1800

 WHICH IMPLIES ∠KHB=1800−68.50=111.50

SINCE CH=CB, THUS ΔCHB IS ISOSCLELES AND THUS,

∠CHB=∠ABC=68.50

SINCE THE ANGLES ARE ADJACENT, ∠CHB+∠CHK=∠BHK

∠CHK=111.50−68.50=430

∠CHK=430