Question

what is m∠sut? m∠sut = °

Explanation:

Step1: Use the Angle Bisector Theorem (HL Congruence)

Since the two right - angled triangles (with right angles at the intersection points of the perpendiculars and the sides) have equal hypotenuses (marked with the same tick) and share the side \(SU\), by the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, the two angles \(x + 63^{\circ}\) and \(4x\) are equal. So, we set up the equation \(x+63 = 4x\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(x+63 = 4x\). We get \(63=4x - x\), which simplifies to \(63 = 3x\). Then divide both sides by 3: \(x=\frac{63}{3}=21\).

Step3: Find \(m\angle SUT\)

Since \(m\angle SUT = 4x\), substitute \(x = 21\) into the expression. So \(m\angle SUT=4\times21\).

Answer:

\(84\)