triangle qrs has the angle measures shown. m∠q=(1x)°, m∠r=(3x)°, m∠s=(6x)°. what is the measure of the…

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

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

Answer

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

(10x = 180).

Step3: Solve for (x)

Divide both sides of the equation 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