Question

find the value of the variable.
16, q, 36, 28
q = \square

Explanation:

Step1: Apply the Angle Bisector Theorem

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the adjacent sides. So, we have the proportion $\frac{q}{16}=\frac{36}{28}$.

Step2: Solve the proportion for \(q\)

Cross - multiply: \(28q = 16\times36\). Then \(28q=576\). Divide both sides by 28: \(q=\frac{576}{28}=\frac{144}{7}\approx20.57\).

Answer:

\(q = \frac{144}{7}\)