Question

The angles of quadrilateral is in the ratio of 4:8:12:16 find the measures of each angles.

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Answer 1

Given :

• The angles of quadrilateral is in the ratio of 4:8:12:16.

To find :

• The measures of each angles =?

Step-by-step explanation :

Let, the angles of quadrilateral are 4x, 8x, 12x and 16x.

As We know that,

Sum of all angles of quadrilateral = 360°

So,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values, we get,

➮ 4x + 8x + 12x + 16x = 360°

➮ 40x = 360°

➮ x = 360° / 40

➮ x = 9°.

Therefore, We get the value of, x = 9°.

Hence,

Value of ∠A , 4x = 4 × 9° = 36°

Value of ∠B , 8x = 8 × 9° = 72°

Value of ∠C , 12x = 12 × 9° = 108°

Value of ∠D , 16x = 16 × 9° = 144°

Verification :

As We know that :

Sum of all angles of quadrilateral = 360°

So,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values, we get,

36° + 72° + 108° + 144° = 360°

360° = 360°

LHS = RHS

Hence, it is verified.