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Question

# Explain how to find the measure of an unknown acute angle in a right triangle.

Solution

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If the other acute angle is given $\alpha$ then we know that, sum of internal angles of a triangle is $180\text{\textdegree}$.

Let the unknown angle is $\theta$.

\begin{align*} \implies \theta+\alpha+90\text{\textdegree}&=180\text{\textdegree}\\ \implies \theta+\alpha&=180\text{\textdegree}-90\text{\textdegree}\\ \implies \theta&=90\text{\textdegree}-\alpha\\ \end{align*}

So, the unknown acute angle is $\left(90\text{\textdegree}-\text{known acute angle}\right)$.

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