Question

In a quadrilateral EFGH. angle EHG is thrice of angle HGF,angle GFE= 70 degree and HE is perpendicular to EF. FIND ANGLE EHG AND ANGLE HGF.

Answer 1

Concept we will be using:
i) Sum of angles of a quadrilateral is 360°
ii) Angle between two perpendicular lines is 90°
---------------------------------------------------------------------------
Solution:
Let ∠HGF=x°
Then, ∠EHG=thrice ∠HGF= 3x°

Also, given ∠GFE=70°
And, HE is perpendicular to EF, then∠HEF=90°

Sum  of angles in a quadrilateral is 360°.
Therefore,
∠HGF + ∠EHG + ∠GFE +∠HEF=360
Plug in the values:
⇒x+3x+70+90=360
⇒4x+160=360
Subtract 160 from both sides:
⇒4x=360-160
⇒4x=200
Divide both sides by 4:
⇒x=50

∠HGF=x°=50°

∠EHG= 3x°=3(50)=150°


Answer: ∠HGF = 50° and ∠EHG = 150°