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Find the value of the unknown exterior angle $x$ in the following diagrams:
"
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) $\angle BAC+\angle ABC=x$
$\Rightarrow 30^{\circ}+60^{\circ}=x$
$\Rightarrow x=90^{\circ}$