what is m∠h? m∠h =

Explanation:

Step1: Recall inscribed - angle property

In a circle, angles inscribed in the same arc are equal. Also, the sum of opposite angles of a cyclic quadrilateral is 180°. Here, angles at (I) and (H) are opposite angles of a cyclic quadrilateral (IJHK). So, ((9x + 8)+11x=180).

Step2: Solve the equation for (x)

Combine like - terms: (9x+11x + 8=180), which gives (20x+8 = 180). Subtract 8 from both sides: (20x=180 - 8=172). Then divide both sides by 20: (x=\frac{172}{20}=8.6).

Step3: Find the measure of (\angle H)

Substitute (x = 8.6) into the expression for (m\angle H). Since (m\angle H=11x), then (m\angle H=11\times8.6 = 94.6^{\circ}).

Answer:

(94.6)