Question

The acute angles of a right triangle have a ratio of $2:3$. What is the difference between the two angle measures?

• A. $42$ degrees
• B. $54$ degrees
• C. $18$ degrees
• D. $72$ degrees

Answer 1

The correct option is C $18$ degrees

Use the fact that the sum of the angles in any triangle $={180}^o$ degrees.

Let the measure of angle be $2x$ and $3x$

$2x+3x+{90}^o={180}^o$ (Combine like-terms).

$\Rightarrow 5x+{90}^o={180}^o$ (Subtract $90$ from both sides).

$\Rightarrow 5x={90}^o$ (Divide both sides by $5$).

$\Rightarrow x={18}^o$

$\Rightarrow 2x={36}^o$

$\Rightarrow 3x={54}^o$

The measures of the acute angles in a right triangle whose ratio is $2:3$ are:

$36$ degrees and $54$ degrees.

Therefore, difference between the two angles $={54}^o-{36}^o={18}^o$

Hence, option C is correct.