Question

triangle qrs has the angle measures shown. m∠q=(1x)°, m∠r=(3x)°, m∠s=(6x)°. what is the measure of the obtuse angle? 18 54 108 216

Explanation:

Step1: Use angle - sum property of a triangle

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

Step2: Combine like - terms

\(1x+3x + 6x=(1 + 3+6)x=10x\). So, \(10x = 180\).

Step3: Solve for \(x\)

Dividing both sides of the equation \(10x = 180\) by 10, we get \(x=\frac{180}{10}=18\).

Step4: Find the measure of each angle

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

Step5: Identify the obtuse angle

An obtuse angle is an angle whose measure is greater than 90° and less than 180°. So the obtuse angle is \(m\angle S = 108^{\circ}\).

Answer:

108