If Delta XYZ sim Delta DEF for the correspond | vedclass

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(C) Given that $\Delta XYZ \sim \Delta DEF$,the corresponding angles are equal: $m \angle X = m \angle D$,$m \angle Y = m \angle E$,and $m \angle Z =

Vedclass · Accepted Answer

$60$

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(C) Given that $\Delta XYZ \sim \Delta DEF$,the corresponding angles are equal: $m \angle X = m \angle D$,$m \angle Y = m \angle E$,and $m \angle Z = m \angle F$.In $\Delta XYZ$,the sum of angles is $180^{\circ}$,so $m \angle X + m \angle Y + m \angle Z = 180^{\circ}$.Given $2 m \angle X = 3 m \angle Y$,we have $m \angle X = 1.5 m \angle Y$.Substituting the values into the sum equation: $1.5 m \angle Y + m \angle Y + 30^{\circ} = 180^{\circ}$.$2.5 m \angle Y = 150^{\circ}$.$m \angle Y = 150^{\circ} / 2.5 = 60^{\circ}$.Since $\Delta XYZ \sim \Delta DEF$,$m \angle E = m \angle Y = 60^{\circ}$.

If $\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow DEF$,and $2 m \angle X = 3 m \angle Y$ with $m \angle Z = 30^{\circ}$,find $m \angle E$. (in $^{\circ}$)

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