Question

what is m∠ghi? m∠ghi = °

Explanation:

Step1: Identify congruent angles

Since the two right - angled triangles have equal hypotenuses (both 66) and share a common side (HF), the two triangles are congruent by the Hypotenuse - Leg (HL) congruence criterion. So, \(4z=5z - 15^{\circ}\).

Step2: Solve for z

Subtract \(4z\) from both sides of the equation \(4z=5z - 15^{\circ}\). We get \(0 = z-15^{\circ}\), then \(z = 15^{\circ}\).

Step3: Find \(m\angle GHI\)

\(m\angle GHI=4z + 5z-15^{\circ}=9z-15^{\circ}\). Substitute \(z = 15^{\circ}\) into the expression. \(m\angle GHI=9\times15^{\circ}-15^{\circ}=(9 - 1)\times15^{\circ}=8\times15^{\circ}=120^{\circ}\).

Answer:

\(120\)