Question

3
m∠r = ____
°
m∠s = ____
°
m∠t = ____
°

Explanation:

Step1: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(x + 7x+4x=180\).

Step2: Combine like - terms

Combining the \(x\) terms on the left - hand side gives \(12x = 180\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(12x = 180\) by 12, we get \(x=\frac{180}{12}=15\).

Step4: Find the measure of each angle

For \(\angle R\), since \(m\angle R=x^{\circ}\), then \(m\angle R = 15^{\circ}\).
For \(\angle S\), since \(m\angle S = 7x^{\circ}\), then \(m\angle S=7\times15 = 105^{\circ}\).
For \(\angle T\), since \(m\angle T = 4x^{\circ}\), then \(m\angle T=4\times15 = 60^{\circ}\).

Answer:

\(m\angle R = 15^{\circ}\)
\(m\angle S = 105^{\circ}\)
\(m\angle T = 60^{\circ}\)