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In the figure given below AB=AC ,Ch=CB and HK is parallel to BC if angle C A X is 140 degree then angle H C K is? please email step by step |
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Answer» Step-by-step EXPLANATION:In the adjoining figureAB=AC,CH=CBHK∥BCIf ∠CAD=137 ∘ , FIND ∠CHKGiven : AB=AC,CH=CB and HK∥BCTO FIND: ∠CHKSINCE AB=AC THUS, ΔABC IS ISOSCELES.∠DAC IS THE EXTERNAL ANGLE, WHICH EQUALS SUM OF OPPOSITE INTERIOR ANGLES:∠DAC=∠ABC+∠ACB⇒137 0 =2∠ABC[∠ABC=∠ACB]⇒∠ABC=68.5 0 SINCE HK∥BC,∠KHB+∠HBC=180 0 WHICH IMPLIES ∠KHB=180 0 −68.5 0 =111.5 0 SINCE CH=CB, THUS ΔCHB IS ISOSCLELES AND THUS,∠CHB=∠ABC=68.5 0 SINCE THE ANGLES ARE ADJACENT, ∠CHB+∠CHK=∠BHK∠CHK=111.5 0 −68.5 0 =43 0 ∠CHK=43 0 |
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