Question

question for genius rank and moderator rank​

Answer 1

Step-by-step explanation:

❍ Given :

• Ratio of the angles of a quadrilateral is 3:5:9:13

❍ To Find :

• Angles of the quadrilateral

❍ Solution :

★ Let the angles be 3x, 5x, 9x and 13x.

Sum of all the angles of a quadrilateral is 360°.

➠ 3x + 5x + 9x + 13x = 360°

➠ 30x = 360°

➠ x = 360/30

➠ x = 12

Value of x is 12.

❒ The angles are :

◘ 3x = 3 × 12 = 36°

◘ 5x = 5 × 12 = 60°

◘ 9x = 9 × 12 = 108°

◘ 13x = 13 × 12 = 156°

∴ The angles of a quadrilateral are 36°, 60°, 108° and 156°.

❍ Verification :

⇛ 36° + 60°+ 108° + 156° = 360°

⇛ 360° = 360°

Hence, Verified.

Answer 2

Answer :

Firstly,

Let,

The angles of quadiarallel will be 3x, 5x, 9x and 13x

and

we know that,

Sum of angles of quadiarallel = 360°

According to the Question :

$\: \: \: \: \sf \: 3x + 5x + 9x + 13x = 360^{ \circ} \\ \sf \implies \: \: 30x = 360^{ \circ} \\ \sf \implies \: x = 12^{ \circ} \\ \\ \bf \: now \\ \green \odot \sf \: value \: of \: \: 3x = 3 \times 12 = 36^{ \circ} \\ \\ \green \odot\sf \: value \: of \: \: 5x = 5 \times 12 = 60^{ \circ} \\ \\ \green \odot\sf \: value \: of \: \: 9x = 9 \times 12 = 108^{ \circ} \\ \\ \green \odot\sf \: value \: of \: \: 13x = 13 \times 12 = 156^{ \circ} \\ \:$

Therefore, the angles are 36°, 60°, 108° and 156° .