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​

Answers

Answer 1

Answer:

x = [tex]30^{o}[/tex]

Explanation:

The sum of the interior angles of a quadrilateral is [tex]360^{o}[/tex], so that from the given question:

<A + <B + <C + <D = [tex]360^{o}[/tex]

(2x + 35) + (3x - 5) + (x + 10) + (4x + 20) = [tex]360^{o}[/tex]

10x + 60 = [tex]360^{o}[/tex]

10x = [tex]360^{o}[/tex] - 60

     = 300

x = [tex]\frac{300}{10}[/tex]

  = 30

x = [tex]30^{o}[/tex]

So that,

<A = (2x + 35) = (2*30 + 35) = [tex]95^{o}[/tex]

<B = (3x - 5) = (3*30 - 5) = [tex]85^{o}[/tex]

<C = (x + 10) = (30 + 10) = [tex]40^{o}[/tex]

<D = (4x + 20) = (4*30 + 20) = [tex]140^{o}[/tex]

Thus,

[tex]95^{o}[/tex] + [tex]85^{o}[/tex] + [tex]40^{o}[/tex] + [tex]140^{o}[/tex] = [tex]360^{o}[/tex]


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