Question

The acute angles of a right triangle have a ratio of $12:3.$ What is the difference between the two angle measures?

• A. ${42}^{\circ }$
• B. ${54}^{\circ }$
• C. ${64}^{\circ }$
• D. ${72}^{\circ }$

Answer 1

The correct option is B ${54}^{\circ }$

Let the measure of acute angles be $12x$ and $3x$ respectively.

Now, we will apply the angle sum property of a triangle,

$12x+3x+90=180$

$\Rightarrow 15x+{90}^{\circ }={180}^{\circ }$

$\Rightarrow 15x={90}^{\circ }$

$\Rightarrow x=6^{\circ }$

So,

$\Rightarrow 12x=12\times 6^{\circ }$

$={72}^{\circ }$

$\Rightarrow 3x=3\times 6^{\circ }$

$={18}^{\circ }$

Therefore, the acute angles are ${72}^{\circ }$ and ${18}^{\circ }$ degrees.

The difference between these angles is ${72}^{\circ }-{18}^{\circ }={54}^{\circ }.$