Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

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

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

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

An obtuse angle is an angle with a measure greater than \(90^{\circ}\) and less than \(180^{\circ}\).

Answer:

\(108\)