Explanation
We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$= 20^{\circ}$$.
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-20^o$$ $$=70^o.$$
$$\therefore$$ Measure of a complementary angle of $$20^{\circ}$$ $$= 70^{\circ}$$.
Therefore, option $$B$$ is correct.
If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $$180^\circ$$ which is also known as a linear pair.
Consider the given triangle, we can easily apply exterior angle property of triangle.
For given triangle $$XYZ$$,
$$\angle 1+\angle 2+\angle z=180^{o}$$
Also, $$\angle 3+\angle z=180^{o}$$ ......... (Linear pair of angles)
$$\angle 1+\angle 2+\angle z=\angle 3 +\angle z$$
$$\Rightarrow \angle 3=\angle 1+\angle 2$$ ...... (which is the Exterior angle property).
Therefore, we can say that, an exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Hence, option $$A$$ is correct.
We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.
Here,
the sum, $$\angle 2+\angle 3$$, is vetrically opposite to a perpendicular.
Given, measure of one complementary angle is $$12.7^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-12.7^o$$ $$=77.3^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 12.7^{o}=77.3^o$$.
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