Question

two angles form a linear - pair. the measure of one angle is 11 times the measure of the other angle. what is the measure of the larger angle? a) 82.5° b) 81.8° c) 163.6° d) 165°

Explanation:

Step1: Define the angles

Let one angle be $x$. Then the other is $11x$.

Step2: Use linear - pair property

Since they form a linear pair, $x + 11x=180^{\circ}$.

Step3: Solve the equation

Combining like - terms gives $12x = 180^{\circ}$, so $x=\frac{180^{\circ}}{12}=15^{\circ}$.

Step4: Find the larger angle

The larger angle is $11x$. Substituting $x = 15^{\circ}$, we get $11\times15^{\circ}=165^{\circ}$.

Answer:

D. $165^{\circ}$