question_answer

(a) Find the angle which is equal to its complement.

(b) Find the angle which is equal to its supplement.

Answer:

(a) Let the measure of the angle be\[x{}^\circ \]. Then, the measure of its complement is given to\[90{}^\circ x{}^\circ \].

Since, the angle is equal of its complement.

\[x{}^\circ =90{}^\circ x{}^\circ \]

On transposing \[x{}^\circ \]from RHS to LHS, we get

\[x{}^\circ +x{}^\circ =90{}^\circ \]

\[2x{}^\circ =90{}^\circ \Rightarrow x{}^\circ =45{}^\circ \]

(b) Let the angles be\[x{}^\circ \].

Therefore, its supplement be 180° ? x°.

Since, the angle is equal to it supplement.

∴ \[x{}^\circ =180{}^\circ x{}^\circ \]

On transposing x° from RHS to LHS, we get

\[x{}^\circ +x{}^\circ =180{}^\circ \]

\[2x{}^\circ =180{}^\circ \]

On dividing both by 2, we get

∴ \[x{}^\circ =\frac{180{}^\circ }{2}=90{}^\circ \]