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

Question

The triangle ABC is shown below.

angle $∢A=70°$ .

$\frac{∢B}{∢C}=\frac{1}{3}$

Calculate angle $∢C$ .

00:00 Calculate angle C

00:03 Angle ratio according to the given data

00:05 Isolate angle C

00:21 Let's mark angle B's value as A

00:31 Substitute the angle expressions in the triangle

00:40 Sum of angles in a triangle equals 180

00:45 Group terms and isolate the value of angle A

01:11 This is the value of angle A, now let's substitute in the expression for angle C

01:20 And this is the solution to the question

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 $82.5^\circ$ .

82.5°