Triangle Angle Problem: Finding Angle A = 3(B + C)

To solve this problem, we'll follow these steps:

• Step 1: Use the angle sum property of triangle $ABC$.
• Step 2: Set up an equation using the condition that $∢A = 3(∢B + ∢C)$.
• Step 3: Solve the equations to find $∢A$.

Now, let's work through each step:
Step 1: According to the angle sum property of a triangle:
$∢A + ∢B + ∢C = 180^\circ$ Step 2: We are given $∢A = 3(∢B + ∢C)$. Substitute this relationship into the equation from Step 1:
$3(∢B + ∢C) + ∢B + ∢C = 180^\circ$ Step 3: Simplify the equation:
Start by letting $∢B + ∢C = x$, then $∢A = 3x$. Substitute into the equation:
$3x + x = 180^\circ$ $4x = 180^\circ$ Solving for $x$:
$x = \frac{180^\circ}{4} = 45^\circ$ So, $∢B + ∢C = 45^\circ$. Since $∢A = 3x$:
$∢A = 3 \times 45^\circ = 135^\circ$

Therefore, the measure of angle $∢A$ is $\mathbf{135^\circ}$.