Question

If one angle of a right angled triangle measures ${25}^{\circ },$ then find the measure of the other acute angle.

• A. ${50}^{\circ }$
• B. ${55}^{\circ }$
• C. ${65}^{\circ }$
• D. ${70}^{\circ }$

Answer 1

The correct option is C

${65}^{\circ }$

By angle sum property of a triangle,
$\angle A+\angle B+\angle C={180}^{\circ }$

On substituting the values,
$\angle A+{25}^{\circ }+{90}^{\circ }={180}^{\circ }$
$\angle A+{115}^{\circ }={180}^{\circ }$
$\angle A={180}^{\circ }-{115}^{\circ }$
$\angle A={65}^{\circ }$

Alternate solution:
We know that, in a right angled triangle, the sum of the angles other than ${90}^o$ will be complementary to each other.

So,
$\angle A+\angle C={90}^o$
$\angle A={90}^{\circ }-\angle C$
$={90}^{\circ }-{25}^{\circ }$
$={65}^{\circ }$