Question

II. Answer very Shortly
8. The angles of a quadrilateral ABCD are in the ratio 3:5:9:13. Find all the angles.​

Answer 1

Explanation:

total angle is 360°

so 3+5+9+13=30

so 360/30 is 12

so all angles are

36,60,108,156

mark as brainliest for answering

Answer 2

Given : ↴

$\sf Four \: angles \: of \:a \: quadrilateral \:(ABCD)\: are \: in \: the \: ratio \: 3 : 5: 9 : 13.$

To find : ↴

$\sf \: We \: have \: to \: find \:all \: the \: angles.$

$\bf \underline{\underline{Solution } }$

$\sf \: Let, the \: four \: angles \: of \: a \: quadrilateral \: be, 3x, \: 5x, \: 9x \: and \: 13x.$

$\bf \underline{We \: know \: that },$

$\sf Angle \: sum \: property \: of \: a \: quadrilateral = 360 ^{\circ}$

$\sf \: So, \: 3x \: + \: 5x \: + \: 9x \: + \: 13x \: = \: 360^{\circ}$

$\sf \implies \: 30x \: = \: 360^{\circ}$

$\sf \implies \: x \: = \: \dfrac{360}{30}$

$\sf \implies \: x \: = 12$

$\sf \: \underline{Hence \: the \: angles \: of \: the \: quadrilateral \: are} \: :$

$\sf \implies 1^{st} \: angle = 3x \: = \: 3 \times 12 \: = \: 36^{\circ}$

$\sf \implies 2^{nd} \: angle = 5x \: = \: 5 \times 12 \: = \: 60^{\circ}$

$\sf \implies 3^{rd} \: angle = 9x \: = \: 9 \times 12 \: = \: 108^{\circ}$

$\sf \implies 4^{th} \: angle = 13x \: = \: 13 \times 12 \: = \: 168^{\circ}$

$\sf \therefore \: \underline{The\: length \:of \:four \:angles \: of \: a \: quadrilateral\: are\: }:$

$\sf \implies \purple{36^{\circ},\: 60 ^{\circ},\: 108 ^{\circ} \:and \:156 ^{\circ}.}$

Extra information : ↴

In quadrilateral 'quad' mean four and 'lateral' means sides. A quadrilateral is a closed figure made up of four segments. In other words it is a polygon with four sides. It has four sides, four vertex and four angles.