Question

if the angles of a quadrilateral are (2x°) (5x+10°) (4x+10°) and(2x+15°) then find the angles

Answer 1

Given angles of quadrilateral are

• 2x
• 5x+10
• 4x+10
• 2x+15

We know

$\boxed{\sf Sum\:of\:angles\:of\;Quadrilateral =360°}$

$\\ \sf\longmapsto 2x+(5x+10)+(4x+10)+(2x+15)=360$

$\\ \sf\longmapsto 2x+5x+10+4x+10+2x+15=360$

$\\ \sf\longmapsto 2x+5x+4x+2x+10+10+15=360$

$\\ \sf\longmapsto 13x+35=360$

$\\ \sf\longmapsto 13x=360-35$

$\\ \sf\longmapsto 13x=325$

$\\ \sf\longmapsto x=\dfrac{325}{13}$

$\\ \sf\longmapsto x=25$

Angles are

$\\ \sf\longmapsto 2x=2(25)=50°$

$\\ \sf\longmapsto 5x+10=5(25)+10=135°$

$\\ \sf\longmapsto 4x+10=4(25)+10=110°$

$\\ \sf\longmapsto 2x+15=2(25)+15=65°$

Answer 2

Answer:

in any quadrilateral sum of all angles

so , (2x) + (5x+10) + (4x+10) +(2x+15) =360

(2x + 5x +4x + 2x) +(10 + 10+15)=360

13x+35=360

13x=360-35

13x=325

x=325/13

x=25

Step-by-step explanation:

2x=50

5x+10=135

4x+10=110

2x+15=65