Question

In a quadrilateral ABCD,the angles A,B,C and D are in the ratio 1: 2 :3 : 4. What is the measure of the

smallest angle?​

Answer 1

Answer:

∠A = 36°; ∠B = 72°; ∠C = 108°; ∠D  = 144°

Step-by-step explanation:

Given that the ratio of measures of interior angles of a quadrilteral is given by 1:2:3:4

let x be the proportion

=> ∠A = x ; ∠B=2x ; ∠C=3x ; ∠D=4x

we know that sum of the angles of a quadrilateral = 360°

=> ∠A+∠B+∠C+∠D = 360°

=> x+2x+3x+4x = 360°

=> 10x = 360°

=> x=36

=> the angles are

∠A = 36°

∠B = 2*36° = 72°

∠C = 3*36° = 108°

∠D = 4*36° = 144°

Answer 2

Answer :

∠A = 36° is the smallest angle

Step-by-step explanation:

Given that the ratio of measures of interior angles of a quadrilteral is given by 1:2:3:4

let x be the proportion

⟹ ∠A = x ; ∠B=2x ; ∠C=3x ; ∠D=4x

we know that sum of the angles of a quadrilateral = 360°

⟹ ∠A+∠B+∠C+∠D = 360°

⟹ x+2x+3x+4x = 360°

⟹ 10x = 360°

⟹ x=36

$\therefore$ The angles are :

∠A = 36°

∠B = 2*36° = 72°

∠C = 3*36° = 108°

∠D = 4*36° = 144°