# Find the value of the unknown $x$ in the following diagrams:"

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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 13:34:19