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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

Question

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

Answer

4.3 (266 Votes)
Verificación de expertos
Valerie Elite · Tutor for 8 years

Answer

Let's evaluate each statement one by one:1. If , then .Since is a right triangle with being the right angle, the sum of the angles in a triangle is . Therefore, . Given and (since it's a right angle), we can find 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, . This statement is true.2. If , then .This statement is false because is a right angle, which means , not .3. If and , then .This statement cannot be true because is a right angle, which means . The given condition is incorrect for a right triangle. Therefore, any conclusion drawn from this incorrect information is invalid.4. If and , then .Again, this statement is incorrect because is a right angle, which means . The given condition is incorrect for a right triangle.5. If and , then .This statement is false because is a right angle, which means . Additionally, the sum of the angles in a triangle cannot exceed , so cannot be .In conclusion, the only true statement is the first one:If , then .