Question

08. The angles of a quadriletenal
of each angle
the ratio
in
measure
1:2: 3:4. Find the
you​

Answer 1

Step-by-step explanation:

The sum of interior angles of a quadrilateral(say, ABCD)=360°

∠A+∠B+∠C+∠D=360°∠A+∠B+∠C+∠D=360°

The sum of exterior angles = 360°

∠1+∠2+∠3+∠4=360°∠1+∠2+∠3+∠4=360°

Source: Google Images

Let the common ratio be x. Then

∠1+∠2+∠3+∠4=1x+2x+3x+3x=360°∠1+∠2+∠3+∠4=1x+2x+3x+3x=360°

⇒x=40°⇒x=40°

⇒∠1=40°⇒∠1=40°

∠2=80°∠2=80°

∠3=120°∠3=120°

∠4=120°∠4=120°

Interior angle+exterior angle =180°

Interior angle= 180°- exterior angle

∠A=180°−∠1=180°−40°=140°∠A=180°−∠1=180°−40°=140°

∠B=180°−∠2=180°−80°=100°∠B=180°−∠2=180°−80°=100°

∠C=180°−∠3=180°−120°=60°∠C=180°−∠3=180°−120°=60°

∠D=180°−∠4=180°−120°=60°∠D=180°−∠4=180°−120°=60°...