Question

In a right angle $\Delta$, if one acute angle measures $x^{\circ }$, then the measure of the other acute angle is ___

• A. $\frac{x}{2}$
• B. $x$
• C. $({180}^{\circ }-x^{\circ })$
• D. $({90}^{\circ }-x^{\circ })$

Answer 1

The correct option is D

$({90}^{\circ }-x^{\circ })$

In a right angle triangle, the two acute angles are complementary, i.e., their measures add upto ${90}^{\circ }$.$\therefore$ If one acute angle measures $x^{\circ }$, the other acute angle will measure ${90}^{\circ }-x^{\circ }$.

Hence, (D)

Alternate:

$\angle \text{A}+x+{90}^{\circ }={180}^{\circ }$

$\therefore \angle \text{A}={180}^{\circ }-{90}^{\circ }-x$

$={90}^{\circ }-x^{\circ }$