Select all the statements that are true about Delta MKH If mangle M=38^circ then mangle DHM=52^circ If mangle M=38^circ then mangle K=52^circ If mangle K=47 and mangle M=21^circ then mangle MHK=112^circ If mangle K=63^circ and mangle M=17^circ then mangle MHK=80^circ If mangle M=55^circ and mangle KHM=103^circ then mangle K=158^circ

Let's evaluate each statement one by one:1. If \(m \angle M=38^{\circ}\), then \(m \angle DHM=52^{\circ}\).Since \(\triangle MKH\) is a right triangle with \(\angle K\) being the right angle, the sum of the angles in a triangle is \(180^{\circ}\). Therefore, \(m \angle M + m \angle K + m \angle H = 180^{\circ}\). Given \(m \angle M = 38^{\circ}\) and \(m \angle K = 90^{\circ}\) (since it's a right angle), we can find \(m \angle H\) as follows:\(m \angle H = 180^{\circ} - (m \angle M + m \angle K) = 180^{\circ} - (38^{\circ} + 90^{\circ}) = 180^{\circ} - 128^{\circ} = 52^{\circ}\).Therefore, \(m \angle DHM = m \angle H = 52^{\circ}\). This statement is true.2. If \(m \angle M=38^{\circ}\), then \(m \angle K=52^{\circ}\).This statement is false because \(\angle K\) is a right angle, which means \(m \angle K = 90^{\circ}\), not \(52^{\circ}\).3. If \(m \angle K=47^{\circ}\) and \(m \angle M=21^{\circ}\), then \(m \angle MHK=112^{\circ}\).This statement cannot be true because \(\angle K\) is a right angle, which means \(m \angle K = 90^{\circ}\). The given condition \(m \angle K=47^{\circ}\) is incorrect for a right triangle. Therefore, any conclusion drawn from this incorrect information is invalid.4. If \(m \angle K=63^{\circ}\) and \(m \angle M=17^{\circ}\), then \(m \angle MHK=80^{\circ}\).Again, this statement is incorrect because \(\angle K\) is a right angle, which means \(m \angle K = 90^{\circ}\). The given condition \(m \angle K=63^{\circ}\) is incorrect for a right triangle.5. If \(m \angle M=55^{\circ}\) and \(m \angle KHM=103^{\circ}\), then \(m \angle K=158^{\circ}\).This statement is false because \(\angle K\) is a right angle, which means \(m \angle K = 90^{\circ}\). Additionally, the sum of the angles in a triangle cannot exceed \(180^{\circ}\), so \(m \angle K\) cannot be \(158^{\circ}\).In conclusion, the only true statement is the first one:If \(m \angle M=38^{\circ}\), then \(m \angle DHM=52^{\circ}\).