Question

While calculating the two acute angles of a right angled triangle, Rehaan found them to be measuring ${60}^{\circ }$ and ${20}^{\circ }$ while Kavya found them to be measuring ${65}^{\circ }$ and ${25}^{\circ }$ .
Select the correct statement from the following:

• A. Kavya's measurement is accurate while Rehaan's is not.
• B. Rehaan's measurement is accurate while Kavya's is not.
• C. Both have measured correctly.
• D. Both have measured incorrectly.

Answer 1

The correct option is A Kavya's measurement is accurate while Rehaan's is not.

Sum of angles of a triangle
$={180}^{\circ }$

Since, we already know that the measure of one angle of the right angled triangle is (${90}^{\circ }$). The sum of the other two angles should be ${180}^{\circ }-{90}^{\circ }={90}^{\circ }$

Angles measured by Rehaan are $({60}^{\circ },{20}^{\circ })$

$Sum={60}^{\circ }+{20}^{\circ }={80}^{\circ }$
which does not add upto ${90}^{\circ }$.

$\therefore$ Rehaan has measured the angles incorrectly.

Angles measured by Kavya are $({65}^{\circ },{25}^{\circ })$

$Sum={65}^{\circ }+{25}^{\circ }={90}^{\circ }$
Hence, kavya has measured the angles correctly.