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]
