In a quadrilateral EFGH,angle EHG is thrice of angleHGF, angleGFE =70 and HE is perpendicular to EF Find the - Maths - Quadrilaterals

Question

In a quadrilateral EFGH,angle EHG is thrice of angleHGF, angleGFE
=70° and HE is perpendicular to EF Find the measure of angleEHG
and angleHGF

Rajat Sethi · Accepted Answer

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Given,∠GFE=70°∠EHG=3∠HGF
(i)Also,HE⊥EF∴∠HEF=90°In a quadrilateral sum of all the angles =360°⇒∠HEF+∠GFE+∠EHG+∠HGF=360°⇒90°+70°+3∠HGF+∠HGF=360°
[Using (i)]⇒4∠HGF=360°-160°⇒∠HGF=200°4=50°∴∠EHG=3×50°=150°

In a quadrilateral EFGH,angle EHG is thrice of angleHGF, angleGFE =70° and HE is perpendicular to EF.Find the measure of angleEHG and angleHGF.