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

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To do:

We have to find the unknown exterior angle $x$ in each case.

Solution:

For convenience, we shall name all the triangles given in the diagram as $\triangle ABC$.

We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Therefore,

(i) $\angle BAC+\angle ABC=x$

$\Rightarrow 70^{\circ}+\ 50^{\circ}=x$

$\Rightarrow x=120^{\circ}$

(ii) $\angle BAC\ +\angle ACB=x$

$\Rightarrow 65^{\circ}+45^{\circ}=x$

$\Rightarrow x=110^{\circ}$

(iii) $\angle CAB+\angle ABC=x$

$\Rightarrow 30^{\circ}+40^{\circ}=x$

$\Rightarrow x=70^{\circ}$

(iv) $\angle BCA+\angle BAC=x$

$\Rightarrow 60^{\circ}+60^{\circ}=x$

$\Rightarrow x=120^{\circ}$

(v) $\angle BAC+\angle ABC=x$

$\Rightarrow 50^{\circ}+50^{\circ}=x$

$\Rightarrow x=100^{\circ}$

(vi) $\angle BAC+\angle ABC=x$

$\Rightarrow 30^{\circ}+60^{\circ}=x$

$\Rightarrow x=90^{\circ}$

Updated on 10-Oct-2022 13:34:11