Question

a circular flowerbed with center p in a park has two intersecting tangents, kl and km, drawn from a point k outside the circle. the larger intercepted arc measures 232° degrees, and the smaller one measures 128° degrees, as shown. determine the measure of the angle lkm. enter your answer in the box. ∠lkm = \\(\square\\)°

Explanation:

Step1: Recall the tangent - angle formula

The measure of an angle formed by two tangents drawn from an external point to a circle is half the difference of the measures of the intercepted arcs. The formula is $\angle LKM=\frac{1}{2}(\text{measure of larger arc}-\text{measure of smaller arc})$.

Step2: Identify the larger and smaller arcs

The larger intercepted arc measures $232^{\circ}$ and the smaller intercepted arc measures $128^{\circ}$.

Step3: Substitute the values into the formula

Substitute the values of the arcs into the formula: $\angle LKM=\frac{1}{2}(232 - 128)$.
First, calculate the difference inside the parentheses: $232-128 = 104$.
Then, multiply by $\frac{1}{2}$: $\frac{1}{2}\times104 = 52$.

Answer:

$\angle LKM=\boxed{52}^{\circ}$