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Find the value of the unknown $x$ in the following diagrams:
"
Given: Triangles given in the above diagram with unknown angle $x$.
To do: To find unknown angle $x$ in each case.
Solution:
$(i)$. By using the angle sum property of the triangle
$x+50^{\circ}+60^{\circ}=180^{\circ}$
$\Rightarrow x=180^{\circ}-110^{\circ}$
$\Rightarrow x=70^{\circ}$
$(ii)$. By using the angle sum property of the triangle
$90^{\circ}+30^{\circ}+x=180^{\circ}$
$\Rightarrow x=180^{\circ}-120^{\circ}$
$\Rightarrow x=60^{\circ}$
$(iii)$. By using the angle sum property of the triangle
$30^{\circ}+\ 110^{\circ}+x=180^{\circ}$
$\Rightarrow x=180^{\circ}-140^{\circ}$
$\Rightarrow x=40^{\circ}$
$(iv)$. By using the angle sum property of the triangle
$50^{\circ}+x+x=180^{\circ}$
$\Rightarrow 50^{\circ}+2x=80^{\circ}$
$\Rightarrow x=\frac{130}{2}$
$\Rightarrow x=65^{\circ}$
$(v)$. By using the angle sum property of the triangle
$x+x+x=180^{\circ}$
$\Rightarrow 3x=180^{\circ}$
$\Rightarrow x=\frac{180}{3}$
$\Rightarrow x=60^{\circ}$
$(vi)$. By using the angle sum property of the triangle
$2x+90^{\circ}+x=180^{\circ}$
$\Rightarrow 3x=180^{\circ}-90^{\circ}$
$\Rightarrow x=\frac{90}{3}x$
$\Rightarrow x=30^{\circ}$
Another angle $=2x=2\times30=60^{\circ}$
Updated on: 10-Oct-2022
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