Right Triangle Challenge: Solving for Angles Where ∢A = 4∢B

To solve this problem, we'll systematically go through the following steps:

• Use the sum of angles in a triangle to relate $∢A$ and $∢B$.
• Substitute the given relationship between $∢A$ and $∢B$ into the equation.
• Solve for $∢B$, and then find $∢A$.

First, note that since triangle $ABC$ is right-angled, $∢C = 90^\circ$. Therefore:

$∢A + ∢B + ∢C = 180^\circ$

$∢A + ∢B + 90^\circ = 180^\circ$

This simplifies to:

$∢A + ∢B = 90^\circ$

Given $∢A = 4∢B$, substitute it into the equation:

$4∢B + ∢B = 90^\circ$

Simplify to:

$5∢B = 90^\circ$

Divide by 5:

$∢B = 18^\circ$

Now, using $∢A = 4∢B$:

$∢A = 4 \times 18^\circ = 72^\circ$

Therefore, the calculated angles are $∢B = 18^\circ$ and $∢A = 72^\circ$.

The correct answer is choice 3: $∢B = 18^\circ, ∢A = 72^\circ$.