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, we get $(1x)^{\circ}+(3x)^{\circ}+(6x)^{\circ}=180^{\circ}$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side, we have $(1 + 3+6)x=180$, which simplifies to $10x = 180$.

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

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

Answer:

C. 108