Triangle Angle Calculation: Solving for Angle C Using 1:3 Ratio

To solve this problem, we'll use the properties of a triangle and given ratio:

• Step 1: Let $∢B = x$ and $∢C = 3x$ as per the given ratio $\frac{∢B}{∢C} = \frac{1}{3}$.
• Step 2: Use the triangle sum property: $∢A + ∢B + ∢C = 180^\circ$.
• Step 3: Substitute known values: $70^\circ + x + 3x = 180^\circ$.
• Step 4: Simplify: $4x + 70^\circ = 180^\circ$.
• Step 5: Solve for $x$: $4x = 110^\circ$.
• Step 6: Determine $x$: $x = 27.5^\circ$.
• Step 7: Calculate $∢C$: $∢C = 3x = 3 \times 27.5^\circ = 82.5^\circ$.

Therefore, the measure of angle $∢C$ is $82.5^\circ$.