Explanation
We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.
Consider option $$(A)$$.
The angles are $$30^o$$ and $$150^o$$.
Then their sum $$=30^o+150^o=180^o\ne90^o$$.
Hence, the angles are not complementary.
Consider option $$(B)$$.
The angles are $$76^o$$ and $$14^o$$.
Then their sum $$=76^o+14^o=90^o$$.
Hence, the angles are complementary.
Consider option $$(C)$$.
The angles are $$65^o$$ and $$65^o$$.
Then their sum $$=65^o+65^o=130^o\ne90^o$$.
Consider option $$(D)$$.
The angles are $$120^o$$ and $$30^o$$.
Then their sum $$=120^o+30^o=150^o\ne90^o$$.
Hence, only option $$B$$ is correct.
We know, two angles are complementary when they add up to $$90^o.$$
Given, measure of one complementary angle is $$30^o.$$
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-30^o$$ $$=60^o.$$
$$\therefore$$ Measure of a complementary angle of $$ 30^{o}=60^o$$.
Hence, option $$A$$ is correct.
$$\Rightarrow$$ Measure of other complementary angle $$=90^o-58^o$$ $$=32^o.$$
$$\therefore$$ Measure of the complementary angle of $$ 58^{o}=32^o$$.
Hence, $$ 58^{o}$$ and $$32^o$$ are complements of each other.
That is, if the sum of two angles is $$90^o$$
Therefore, option $$C$$ is correct.
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