Question

triangle qrs has the angle measures shown. what is the measure of the obtuse angle?
$m\angle q=(1x)^{\circ}$
$m\angle r=(3x)^{\circ}$
$m\angle s=(6x)^{\circ}$
18
54
108
216

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle Q + m\angle R+m\angle S=180^{\circ}\). Substituting the given angle expressions: \(1x + 3x+6x=180\).

Step2: Solve for \(x\)

Combine like terms: \(10x = 180\). Then, divide both sides by \(10\): \(x=\frac{180}{10}=18\).

Step3: Find the measure of each angle

\(m\angle Q=(1x)^{\circ}=1\times18 = 18^{\circ}\), \(m\angle R=(3x)^{\circ}=3\times18 = 54^{\circ}\), \(m\angle S=(6x)^{\circ}=6\times18 = 108^{\circ}\).

Answer:

\(108\)