Question

Mathematics class 9
Question-
1. The angles of a Quadrilateral are in ratio 3:5:9:13. Find all angles
2. Show that if the diagonals of a Quadrilateral bisect each other at right angles, then it is a rhombus.
Please step wise step​

Answer 1

3:5:9:13

⇒3x+5x+9x+13x

=360

50x=360

x=12

angle = 36

60 ∘

60∘

108∘

156∘

Step-by-step explanation:

Hope that helps you

Mark my answer in brainlist please:)

Answer 2

$\huge \star \: \underline{ \underline{ \red{ \sf \: solution: }}}$

Question 1.

⍟ Given :

Raito :

• 3:5:9:13

⍟ To Find :

• All angles
• For this , let the angle be = x

⍟ On Solving :

Angles :

• 3x
• 5x
• 9x
• 13x

Angle Sum Property of Quadrilateral

= 360°

$\\ \large \tt \implies \: 3x + 5x + 9x + 13x = 360 \degree \\ \\ \large \implies \tt \: 30x = 360 \degree \\ \\ \\ \large \tt \implies \: x = \frac{360 \degree}{30} \\ \\ \\ \large \star \: \: \underline{ \boxed{ \sf \pink{\therefore \: \: x = 12 \degree}}} \: \: \star$

So, the angles are :

$\\ \large \mapsto \: \underline{ \purple{ \sf \: angle_1 = 3(12 \degree) } = \green{ \: 36 \degree}} \\ \\ \large \mapsto \: \underline{ \purple{ \sf \: angle_2 = 5(12 \degree) } = \green{ \: 60\degree}} \\ \\ \large \mapsto \: \underline{ \purple{ \sf \: angle_3 = 9(12 \degree) } = \green{ \: 108 \degree}} \\ \\ \large \mapsto \: \underline{ \purple{ \sf \: angle_4 = 13(12 \degree) } = \green{ \: 156 \degree}}$

_____________________________________________

⍟ Given :

Let ABCD be a Quadrilateral, where diagonals bisect each other

$\\ \large \therefore \: \: oa$