Question

the three angles of a quadrilateral are in ratio 3:4:5:6 calculate the angles​

Answer 1

Answer:

the angles are 67.5°, 90°, 112.5°, and 90°

Step-by-step explanation:

Let the three angles be 3x, 4x, 5x

It’s is given that

5x - 3x = 45

=> 2x = 45

=> x = 22.5

Therefore the 3 angles are

3*22.5 = 67.5

4*22.5 = 90

5*22.5 = 112.5

According to Angle Sum Property Of Quadrilaterals,

The sum of the 4 angle of a quadrilateral = 360

Let the 4th angle be y

67.5 + 90 + 112.5 + y = 360

=> y = 360 - 270 = 90

Therefore, the angles are 67.5°, 90°, 112.5°, and 90°

Answer 2

Answer:

Let the angles be x

<A=3x°, <B=4x°, <C=5x°, <D=6x°

<A+<B+<C+<D=360°

3x°+4x°+5x°+6x°=360°

18x°=360°

x°=360°/18

x°=20°

<A=3x°=3(20°)=60°,

<B=4x°=4(20°)=80°,

<C=5x°=5(20°)=100°,

<D=6x°=6(20°)=120°.