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: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(m\angle Q + m\angle R+m\angle S=180^{\circ}\).
Substitute \(m\angle Q = x\), \(m\angle R = 3x\), and \(m\angle S = 6x\) into the equation: \(x + 3x+6x=180\).

Step2: Combine like - terms

\((1 + 3+6)x=180\), which simplifies to \(10x = 180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(10x = 180\) by 10: \(x=\frac{180}{10}=18\).

Step4: Find the measure of each angle

\(m\angle Q=x = 18^{\circ}\), \(m\angle R = 3x=3\times18 = 54^{\circ}\), \(m\angle S=6x=6\times18 = 108^{\circ}\).
An obtuse angle is an angle with a measure greater than 90° and less than 180°.

Answer:

C. 108