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