Question

In a quad ABCD Angle A 2x+35 angle B 3x-5 Angle C x+10 Angle D 4x+20 what is the value of x​

Answer 1

x =
`30^(o)`

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is
`360^(o)`, so that from the given question:

<A + <B + <C + <D =
`360^(o)`

(2x + 35) + (3x - 5) + (x + 10) + (4x + 20) =
`360^(o)`

10x + 60 =
`360^(o)`

10x =
`360^(o)` - 60

= 300

x =
`(300)/(10)`

= 30

x =
`30^(o)`

So that,

<A = (2x + 35) = (2*30 + 35) =
`95^(o)`

<B = (3x - 5) = (3*30 - 5) =
`85^(o)`

<C = (x + 10) = (30 + 10) =
`40^(o)`

<D = (4x + 20) = (4*30 + 20) =
`140^(o)`

Thus,

`95^(o)` +
`85^(o)` +
`40^(o)` +
`140^(o)` =
`360^(o)`