Question

Given AHAN = AJMS. If mZH = (3x + 22), mZA== (3x+22)", m_A = (2x+5)°, and m2J = (5x – 16)°,determine mZM.

Answer 1

$\begin{gathered} \Delta HAN\text{ is congruent to }\Delta\text{JMS} \\ \text{Therefore} \\ m\angle H=m\angle j=(5x-16)=(3x+22) \\ m\angle A=m\angle M=(2x+6) \\ m\angle M=? \\ m\angle H=m\angle J \\ 5x-16=3x+22 \\ 5x-3x=22+16 \\ 2x=38 \\ x=\frac{38}{2} \\ x=19 \\ \\ m\angle M=2(19)+6=38+6=44^{\circ} \end{gathered}$