Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle Q + m\angle R + m\angle S = 180^\circ\).
Substitute the given angles: \(x + 3x + 6x = 180\).

Step2: Solve for \(x\)

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

Step3: Find the obtuse angle

An obtuse angle is greater than \(90^\circ\). Calculate each angle:

• \(m\angle Q = x = 18^\circ\)
• \(m\angle R = 3x = 3\times18 = 54^\circ\)
• \(m\angle S = 6x = 6\times18 = 108^\circ\) (this is obtuse as \(108 > 90\)).

Answer:

108