Question

what is m∠fgi? m∠fgi =

Explanation:

Step1: Identify congruent triangles

Since the two right - angled triangles have a common side and equal sides (marked with red dashes), they are congruent by the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles. So, the angles at the vertex \(G\) are equal, i.e., \(4u - 48^{\circ}=2u\).

Step2: Solve for \(u\)

Subtract \(2u\) from both sides of the equation \(4u - 48^{\circ}=2u\):
\(4u-2u-48^{\circ}=2u - 2u\), which simplifies to \(2u-48^{\circ}=0\). Then add \(48^{\circ}\) to both sides: \(2u=48^{\circ}\), and divide both sides by 2: \(u = 24^{\circ}\).

Step3: Find \(m\angle FGI\)

Substitute \(u = 24^{\circ}\) into the expression for \(m\angle FGI\) which is \(4u-48^{\circ}\).
\(m\angle FGI=4\times24^{\circ}-48^{\circ}\)
\(m\angle FGI = 96^{\circ}-48^{\circ}=48^{\circ}\)

Answer:

\(48\)